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Dissertations / Theses on the topic '010101 Algebra and Number Theory'

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Published: 10 December 2022

Last updated: 31 July 2025

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1

PASINI, FEDERICO WILLIAM. "Classifying spaces for knots: new bridges between knot theory and algebraic number theory." Doctoral thesis, Università degli Studi di Milano-Bicocca, 2016. http://hdl.handle.net/10281/129230.

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In this thesis we discuss how, in the context of knot theory, the classifying space of a knot group for the family of meridians arises naturally. We provide an explicit construction of a model for that space, which is particularly nice in the case of a prime knot. We then show that this classifying space controls the behaviour of the finite branched coverings of the knot. We present a 9-term exact sequence for knot groups that strongly resembles the Poitou-Tate exact sequence for algebraic number fields. Finally, we show that the homology of the classifying space behaves towards the former seq

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2

BATTISTONI, FRANCESCO. "APPLICATIONS OF PRIME DENSITIES IN NUMBER THEORY AND CLASSIFICATION OF NUMBER FIELDS WITH BOUNDED INVARIANTS." Doctoral thesis, Università degli Studi di Milano, 2020. http://hdl.handle.net/2434/703505.

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This Ph.D. thesis collects the author's works and interests in several parts of Number Theory, from algebraic problems related to relations between number fields which are based on the factorization of prime numbers in the rings of integers, up to the application of tools concerning the density of primes with given splitting type in number fields to the computation of the average rank of specific families of elliptic curves, concluding finally with the classification and estimate of the main invariants of a number field, like the discriminant and the regulator, pursued by means of analytic for

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3

Bingham, Aram. "Commutative n-ary Arithmetic." ScholarWorks@UNO, 2015. http://scholarworks.uno.edu/td/1959.

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Motivated by primality and integer factorization, this thesis introduces generalizations of standard binary multiplication to commutative n-ary operations based upon geometric construction and representation. This class of operations are constructed to preserve commutativity and identity so that binary multiplication is included as a special case, in order to preserve relationships with ordinary multiplicative number theory. This leads to a study of their expression in terms of elementary symmetric polynomials, and connections are made to results from the theory of polyadic (n-ary) groups. Hig

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4

Sordo, Vieira Luis A. "ON P-ADIC FIELDS AND P-GROUPS." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/43.

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The dissertation is divided into two parts. The first part mainly treats a conjecture of Emil Artin from the 1930s. Namely, if f = a_1x_1^d + a_2x_2^d +...+ a_{d^2+1}x^d where the coefficients a_i lie in a finite unramified extension of a rational p-adic field, where p is an odd prime, then f is isotropic. We also deal with systems of quadratic forms over finite fields and study the isotropicity of the system relative to the number of variables. We also study a variant of the classical Davenport constant of finite abelian groups and relate it to the isotropicity of diagonal forms. The second p

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5

Alnominy, Madai Obaid. "Monomial Progenitors and Related Topics." CSUSB ScholarWorks, 2018. https://scholarworks.lib.csusb.edu/etd/619.

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The main objective of this project is to find the original symmetric presentations of some very important finite groups and to give our constructions of some of these groups. We have found the Mathieu sporadic group M11, HS × D5, where HS is the sporadic group Higman-Sim group, the projective special unitary group U(3; 5) and the projective special linear group L2(149) as homomorphic images of the monomial progenitors 11*4 :m (5 :4), 5*6 :m S5 and 149*2 :m D37. We have also discovered 24 : S3 × C2, 24 : A5, (25 : S4), 25 : S3 × S3, 33 : S4 × C2, S6, 29: PGL(2,7), 22 • (S6 : S6), PGL(2,19),

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6

Salt, Brittney M. "MONOID RINGS AND STRONGLY TWO-GENERATED IDEALS." CSUSB ScholarWorks, 2014. https://scholarworks.lib.csusb.edu/etd/31.

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This paper determines whether monoid rings with the two-generator property have the strong two-generator property. Dedekind domains have both the two-generator and strong two-generator properties. How common is this? Two cases are considered here: the zero-dimensional case and the one-dimensional case for monoid rings. Each case is looked at to determine if monoid rings that are not PIRs but are two-generated have the strong two-generator property. Full results are given in the zero-dimensional case, however only partial results have been found for the one-dimensional case.

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7

Constable, Jonathan A. "Kronecker's Theory of Binary Bilinear Forms with Applications to Representations of Integers as Sums of Three Squares." UKnowledge, 2016. http://uknowledge.uky.edu/math_etds/35.

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In 1883 Leopold Kronecker published a paper containing “a few explanatory remarks” to an earlier paper of his from 1866. His work loosely connected the theory of integral binary bilinear forms to the theory of integral binary quadratic forms. In this dissertation we discover the statements within Kronecker's paper and offer detailed arithmetic proofs. We begin by developing the theory of binary bilinear forms and their automorphs, providing a classification of integral binary bilinear forms up to equivalence, proper equivalence and complete equivalence. In the second chapter we introduce the c

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8

Gopalan, Parikshit. "Computing with Polynomials over Composites." Diss., Georgia Institute of Technology, 2006. http://hdl.handle.net/1853/11564.

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In the last twenty years, algebraic techniques have been applied with great success to several areas in theoretical computer science. However, for many problems involving modular counting, there is a huge gap in our understanding depending on whether the modulus is prime or composite. A prime example is the problem of showing lower bounds for circuits with Mod gates in circuit complexity. Proof techniques that work well for primes break down over composites. Moreover, in some cases, the problem for composites turns out to be very different from the prime case. Making progress on these problem

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9

Munoz, Susana L. "A Fundamental Unit of O_K." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/133.

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In the classical case we make use of Pells equation to compute units in the ring OF. Consider the parallel to the classical case and the quadratic field extension that creates the ring OK. We use the generalized Pell's equation to find the units in this ring since they are solutions. Through the use of continued fractions we may further characterize this ring and compute its units.

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10

COSCELLI, EDOARDO. "STICKELBERGER SERIES AND IWASAWA MAIN CONJECTURE FOR FUNCTION FIELDS." Doctoral thesis, Università degli Studi di Milano, 2018. http://hdl.handle.net/2434/561439.

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Let F be a global function ﬁeld in characteristic p>0. There exists many diﬀerent types of L-functions that can be associated to F, such as the Artin L-functions, the Goss Zeta function or the p-adic L-functions. In this work i have investigated the correlations between these analytic objects and the Stickelberger series, which is a formal power series whose coeﬃcients lie in a suitable Galois algebra. In the second part of this work i have studied the Iwasawa extension generated by the p-torsion of a Hayes module and i have used the Stickelberger series to prove a "main conjecture" for the p-

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11

Fávaro, Eduardo Rogério [UNESP]. "Corpos cujo condutor é potência de primo: caracterização e reticulados ideais associados." Universidade Estadual Paulista (UNESP), 2012. http://hdl.handle.net/11449/100063.

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Made available in DSpace on 2014-06-11T19:30:27Z (GMT). No. of bitstreams: 0 Previous issue date: 2012-08-02Bitstream added on 2014-06-13T18:40:35Z : No. of bitstreams: 1 favaro_er_dr_sjrp.pdf: 449730 bytes, checksum: 66f6b6e8876e035dcd2e6aa8db337bbd (MD5)<br>Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)<br>Este trabalho esta relacionado com a Teoria Algébrica dos Números e aplicações em Reticulados Ideais. Descrevemos os corp os cujo condutor e potência de primo. Quando o primo e dois, descrevemos tamb em o anel de inteiros. Quando o primo e mpar calculamos o discriminante d

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12

Shaughnessy, John F. "Finding Zeros of Rational Quadratic Forms." Scholarship @ Claremont, 2014. http://scholarship.claremont.edu/cmc_theses/849.

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In this thesis, we introduce the notion of quadratic forms and provide motivation for their study. We begin by discussing Diophantine equations, the field of p-adic numbers, and the Hasse-Minkowski Theorem that allows us to use p-adic analysis determine whether a quadratic form has a rational root. We then discuss search bounds and state Cassels' Theorem for small-height zeros of rational quadratic forms. We end with a proof of Cassels' Theorem and suggestions for further reading.

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13

Samson, Duncan Alistair. "An analysis of the influence of question design on pupils' approaches to number pattern generalisation tasks." Thesis, Rhodes University, 2008. http://hdl.handle.net/10962/d1003302.

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This study is based on a qualitative investigation framed within an interpretive paradigm, and aims to investigate the extent to which question design affects the solution strategies adopted by children when solving linear number pattern generalisation tasks presented in pictorial and numeric contexts. The research tool comprised a series of 22 pencil and paper exercises based on linear generalisation tasks set in both numeric and 2-dimensional pictorial contexts. The responses to these linear generalisation questions were classified by means of stage descriptors as well as stage modifiers. Th

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14

Souza, Romario Sidrone [UNESP]. "Equações diofantinas lineares, quadráticas e aplicações." Universidade Estadual Paulista (UNESP), 2017. http://hdl.handle.net/11449/149949.

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Submitted by ROMARIO SIDRONE DE SOUZA null (romario.sidrone@gmail.com) on 2017-03-22T13:09:53Z No. of bitstreams: 1 Equações Diofantinas Lineares, Quadráticas e Aplicações.pdf: 841142 bytes, checksum: 07c262b2dc6963eba6f51b8c68808746 (MD5)<br>Rejected by Luiz Galeffi (luizgaleffi@gmail.com), reason: Solicitamos que realize uma nova submissão seguindo a orientação abaixo: O arquivo submetido não contém o certificado de aprovação. O arquivo submetido está sem a ficha catalográfica. A versão submetida por você é considerada a versão final da dissertação/tese, portanto não poderá ocorre

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15

Truman, Paul James. "Hopf-Galois module structure of some tamely ramified extensions." Thesis, University of Exeter, 2009. http://hdl.handle.net/10036/71817.

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We study the Hopf-Galois module structure of algebraic integers in some finite extensions of $ p $-adic fields and number fields which are at most tamely ramified. We show that if $ L/K $ is a finite unramified extension of $ p $-adic fields which is Hopf-Galois for some Hopf algebra $ H $ then the ring of algebraic integers $ \OL $ is a free module of rank one over the associated order $ \AH $. If $ H $ is a commutative Hopf algebra, we show that this conclusion remains valid in finite ramified extensions of $ p $-adic fields if $ p $ does not divide the degree of the extension. We prove anal

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16

Silva, Paulo Roberto da [UNESP]. "Tópicos de teoria dos números algébricos e aplicações em reticulados e equações diofantinas." Universidade Estadual Paulista (UNESP), 2015. http://hdl.handle.net/11449/134025.

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Made available in DSpace on 2016-02-05T18:29:16Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-08-24. Added 1 bitstream(s) on 2016-02-05T18:33:02Z : No. of bitstreams: 1 000856863.pdf: 777534 bytes, checksum: 909775f1499bec6c0e032d80b0a95b99 (MD5)<br>Neste trabalho é feito um estudo sobre tópicos de Teoria dos Números Algébricos como extensão de corpos, decomposição de ideais primos, corpos quadráticos e ciclotômicos, número de classe e unidade. Nosso principal objetivo é apresentar uma aplicação dessa teoria na construção de reticulados e solução de equações diofantinas<br>This work

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17

Silva, Alexsandro BelÃm da. "FamÃlias infinitas de corpos quadrÃticos imaginÃrios." Universidade Federal do CearÃ, 2010. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=5664.

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FundaÃÃo de Amparo Ã Pesquisa do Estado do CearÃ<br>CoordenaÃÃo de AperfeiÃoamento de Pessoal de NÃvel Superior<br>Seja ℓ > 3 um primo Ãmpar. Sejam So, S+, S_ conjuntos finitos mutuamente disjuntos de primos racionais. Para qualquer nÃmero real suficientemente grande X > 0, baseando-nos em [16], damos neste trabalho, um limite inferior do nÃmero de corpos quadrÃticos imaginÃrios k que satisfazem as seguintes condiÃÃes: o discriminante de k Ã maior que -X o nÃmero de classe de k Ã nÃo divisÃvel por ℓ, todo q â So se ramifica, todo q â S+ se decompÃe e todo q â S_ Ã inerte em k, resp

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18

Santos, Jefferson Marques. "Altura e equidistribuição de pontos algébricos." Universidade Federal de Goiás, 2017. http://repositorio.bc.ufg.br/tede/handle/tede/7564.

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Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-07-05T14:04:12Z No. of bitstreams: 2 Dissertação - Jefferson Marques Santos - 2017.pdf: 1510253 bytes, checksum: fa6dbf92bac6614d3ce705a47bbe41b8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-07-10T14:31:22Z (GMT) No. of bitstreams: 2 Dissertação - Jefferson Marques Santos - 2017.pdf: 1510253 bytes, checksum: fa6dbf92bac6614d3ce705a47bbe41b8 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5)<br>M

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19

Rezola, Nolberto. "Unique Prime Factorization of Ideals in the Ring of Algebraic Integers of an Imaginary Quadratic Number Field." CSUSB ScholarWorks, 2015. https://scholarworks.lib.csusb.edu/etd/205.

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The ring of integers is a very interesting ring, it has the amazing property that each of its elements may be expressed uniquely, up to order, as a product of prime elements. Unfortunately, not every ring possesses this property for its elements. The work of mathematicians like Kummer and Dedekind lead to the study of a special type of ring, which we now call a Dedekind domain, where even though unique prime factorization of elements may fail, the ideals of a Dedekind domain still enjoy the property of unique prime factorization into a product of prime ideals, up to order of the factors. This

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20

Svanström, Fredrik. "Properties of a generalized Arnold’s discrete cat map." Thesis, Linnéuniversitetet, Institutionen för matematik (MA), 2014. http://urn.kb.se/resolve?urn=urn:nbn:se:lnu:diva-35209.

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After reviewing some properties of the two dimensional hyperbolic toral automorphism called Arnold's discrete cat map, including its generalizations with matrices having positive unit determinant, this thesis contains a definition of a novel cat map where the elements of the matrix are found in the sequence of Pell numbers. This mapping is therefore denoted as Pell's cat map. The main result of this thesis is a theorem determining the upper bound for the minimal period of Pell's cat map. From numerical results four conjectures regarding properties of Pell's cat map are also stated. A brief exp

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21

Oliveira, Silvio Barbosa de. "As equações diofantinas lineares e o livro didático de matemática para o ensino médio." Pontifícia Universidade Católica de São Paulo, 2006. https://tede2.pucsp.br/handle/handle/11059.

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Made available in DSpace on 2016-04-27T16:57:42Z (GMT). No. of bitstreams: 1 dissertacao_silvio_barbosa_oliveira.pdf: 371682 bytes, checksum: 4f27d9c132d5173732426c8e48699248 (MD5) Previous issue date: 2006-05-24<br>This work involves a qualitative study of how the theme of linear Diophantine equations is approached in mathematics textbooks for high school students. Using the methods associated with content analysis (Bardin, 1977), I search for references, in both explicit and implicit forms, to these equations in two different sets of high school mathematics textbooks, both of which had bee

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22

Costa, Eduardo Sad da. "As Equações Diofantinas Lineares e o Professor de Matemática do Ensino Médio." Pontifícia Universidade Católica de São Paulo, 2007. https://tede2.pucsp.br/handle/handle/11124.

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Made available in DSpace on 2016-04-27T16:57:53Z (GMT). No. of bitstreams: 1 dissertacao_eduardo_sad_costa.pdf: 3568903 bytes, checksum: 4e09f1b15f7714b64ad56708b0bd9974 (MD5) Previous issue date: 2007-05-21<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior<br>This work involves a qualitative study about whether and how mathematics High-School teachers work with their students the trouble-situations regarding linear Diophantine equations. The study was performed by means of analyzing semi-structured interviews applied on six mathematics teachers from the states of São Paulo and

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23

Amorós, Carafí Laia. "Images of Galois representations and p-adic models of Shimura curves." Doctoral thesis, Universitat de Barcelona, 2016. http://hdl.handle.net/10803/471452.

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The Langlands program is a vast and unifying network of conjectures that connect the world of automorphic representations of reductive algebraic groups and the world of Galois representations. These conjectures associate an automorphic representation of a reductive algebraic group to every n-dimensional representation of a Galois group, and the other way around: they attach a Galois representation to any automorphic representation of a reductive algebraic group. Moreover, these correspondences are done in such a way that the automorphic L-functions attached to the two objects coincide. T

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24

Sofo, Anthony. "Summing series using residues." Thesis, 1998. https://vuir.vu.edu.au/15695/.

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25

(9898418), J. Krausmann. "Archiving of ABC local radio programs." Thesis, 2008. https://figshare.com/articles/thesis/Archiving_of_ABC_local_radio_programs/13465355.

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Studies how many of the thousands of hours of ABC Local Radio programs are being recorded and archived for future reuse, as well as how it is being done, what program makers think about such a task, and how well this proportion can be increased in the near future.

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26

(9872813), D. Black. "Patient-assessed health outcomes in a cycle of continuous quality improvement : a case coronary artery bypass graft surgery." Thesis, 1996. https://figshare.com/articles/thesis/Patient-assessed_health_outcomes_in_a_cycle_of_continuous_quality_improvement_a_case_coronary_artery_bypass_graft_surgery/13416710.

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Thesis argues that patient assessed outcomes and data and records used in health information systems can be used to improve subsequent patient outcomes in a cycle of continous quality improvement.. The problem addressed is whether patient-assessed outcomes can be used to improve subsequent patient outcomes through altering procedures and protocols. Despite a growing awareness amongst some health professionals of the need for "real time science in medicine' -that is, routinely linking patient-assessed outcomes to the processes of care -there are no such studies reported in the literature. A co

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27

Kent, Richard Peabody. "Geometry and algebra of hyperbolic 3-manifolds." Thesis, 2006. http://hdl.handle.net/2152/2732.

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(9910865), Melanie Soo Chin. "Towards a reinterpretation of the radical theory of associative rings using base radical and base semisimple class constructions." Thesis, 2004. https://figshare.com/articles/thesis/Towards_a_reinterpretation_of_the_radical_theory_of_associative_rings_using_base_radical_and_base_semisimple_class_constructions/13417001.

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"This research aims to refresh and reinterpret the radical theory of associative rings using the base radical and base semisimple class constructions. It also endeavours to generalise some results about ideals of rings in terms of accessible subrings. A characterisation of accessible subrings is included. By applying the base radical and base semisimple class constructions to many of the known results in established radical theory a number of gaps are uncovered and closed, with the goal of making the theory more accessible to advanced undergraduate and graduate students and mathematicians in r

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29

Jonck, Elizabeth. "The path partition number of a graph." Thesis, 2012. http://hdl.handle.net/10210/7118.

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Ph.D.<br>The induced path number p(G) of a graph G is defined as the minimum number of subsets into which the vertex set V(G) of G can be partitioned such that each subset induces a path. In this thesis we determine the induced path number of a complete £-partite graph. We investigate the induced path number of products of complete graphs, of the complement of such products and of products of cycles. For a graph G, the linear vertex arboricity lva(G) is defined as the minimum number of subsets into which the vertex set of C can be partitioned so that each subset induces a linear forest. Since

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(9788648), Guy Cooke. "On lower radical type constructions." Thesis, 2010. https://figshare.com/articles/thesis/On_lower_radical_type_constructions/13456742.

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This research is essentially an investigation into lower radical type construction and the consequences thereof. Dealing primarily in associative rings, the aim of this thesis is to construct - and investigate - a generalised lower radical type construction that encapsulates McDougall's base radical class construction and Stewart's strict radical class construction. Beginning with some preliminary results and a brief account of the lower radical (type) constructions in associative rings, we develop the basic concepts and notations used throughout the investigation. After determining a number o

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31

Smith, Harold Justin. "Fractions of Numerical Semigroups." 2010. http://trace.tennessee.edu/utk_graddiss/750.

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Let S and T be numerical semigroups and let k be a positive integer. We say that S is the quotient of T by k if an integer x belongs to S if and only if kx belongs to T. Given any integer k larger than 1 (resp., larger than 2), every numerical semigroup S is the quotient T/k of infinitely many symmetric (resp., pseudo-symmetric) numerical semigroups T by k. Related examples, probabilistic results, and applications to ring theory are shown. Given an arbitrary positive integer k, it is not true in general that every numerical semigroup S is the quotient of infinitely many numerical semigroups of

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Samson, Duncan Alistair. "An analysis of the influence of question design on pupils' approaches to number pattern generalisation tasks /." 2007. http://eprints.ru.ac.za/1121/.

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(9010904), Tyler R. Billingsley. "Effective Injectivity of Specialization Maps for Elliptic Surfaces." Thesis, 2020.

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<pre>This dissertation concerns two questions involving the injectivity of specialization homomorphisms for elliptic surfaces. We primarily focus on elliptic surfaces over the projective line defined over the rational numbers. The specialization theorem of Silverman proven in 1983 says that, for a fixed surface, all but finitely many specialization homomorphisms are injective. Given a subgroup of the group of rational sections with explicit generators, we thus ask the following.</pre><pre>Given some rational number, how can we effectively determine whether or not the associated specialization

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(11186268), Razan Taha. "p-adic Measures for Reciprocals of L-functions of Totally Real Number Fields." Thesis, 2021.

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We generalize the work of Gelbart, Miller, Pantchichkine, and Shahidi on constructing p-adic measures to the case of totally real fields K. This measure is the Mellin transform of the reciprocal of the p-adic L-function which interpolates the special values at negative integers of the Hecke L-function of K. To define this measure as a distribution, we study the non-constant terms in the Fourier expansion of a particular Eisenstein series of the Hilbert modular group of K. Proving the distribution is a measure requires studying the structure of the Iwasawa algebra.

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Irick, Brian C. "On the Irreducibility of the Cauchy-Mirimanoff Polynomials." 2010. http://trace.tennessee.edu/utk_graddiss/707.

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The Cauchy-Mirimanoff Polynomials are a class of polynomials that naturally arise in various classical studies of Fermat's Last Theorem. Originally conjectured to be irreducible over 100 years ago, the irreducibility of the Cauchy-Mirimanoff polynomials is still an open conjecture. This dissertation takes a new approach to the study of the Cauchy-Mirimanoff Polynomials. The reciprocal transform of a self-reciprocal polynomial is defined, and the reciprocal transforms of the Cauchy-Mirimanoff Polynomials are found and studied. Particular attention is given to the Cauchy-Mirimanoff Polynomial

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Amberker, B. B. "Large-Scale Integer And Polynomial Computations : Efficient Implementation And Applications." Thesis, 1996. https://etd.iisc.ac.in/handle/2005/1678.

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Amberker, B. B. "Large-Scale Integer And Polynomial Computations : Efficient Implementation And Applications." Thesis, 1996. http://etd.iisc.ernet.in/handle/2005/1678.

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(11204136), Chris Karl Neuffer. "Genera of Integer Representations and the Lyndon-Hochschild-Serre Spectral Sequence." Thesis, 2021.

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There has been in the past ten to fifteen years a surge of activity concerning the cohomology of semi-direct product groups of the form $\mathbb{Z}^{n}\rtimes$G with G finite. A problem first stated by Adem-Ge-Pan-Petrosyan asks for suitable conditions for the Lyndon-Hochschild-Serre Spectral Sequence associated to this group extension to collapse at second page of the Lyndon-Hochschild-Serre spectral sequence. In this thesis we use facts from integer representation theory to reduce this problem to only considering representatives from each genus of representations, and establish techniques fo

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Elzinga, Randall J. "The Minimum Witt Index of a Graph." Thesis, 2007. http://hdl.handle.net/1974/682.

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An independent set in a graph G is a set of pairwise nonadjacent vertices, and the maximum size, alpha(G), of an independent set in G is called the independence number. Given a graph G and weight matrix A of G with entries from some field F, the maximum dimension of an A-isotropic subspace, known as the Witt index of A, is an upper bound on alpha(G). Since any weight matrix can be used, it is natural to seek the minimum upper bound on the independence number of G that can be achieved by a weight matrix. This minimum, iota_F^*(G), is called the minimum Witt index of G over F, and the resulting

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(10717026), Heng Du. "Arithmetic Breuil-Kisin-Fargues modules and several topics in p-adic Hodge theory." Thesis, 2021.

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<div> <div> <div> <p>Let K be a discrete valuation field with perfect residue field, we study the functor from weakly admissible filtered (φ,N,G<sub>K</sub>)-modules over K to the isogeny category of Breuil- Kisin-Fargues G<sub>K</sub>-modules. This functor is the composition of a functor defined by Fargues-Fontaine from weakly admissible filtered (φ,N,G<sub>K</sub>)-modules to G<sub>K</sub>-equivariant modifications of vector bundles over the Fargues-Fontaine curve X<sub>FF</sub> , with the functor of Fargues-Scholze that between the category of admissible modifications of vector bundles over

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41

(8782541), Dongming She. "Local Langlands Correpondence for the twisted exterior and symmetric square epsilon-factors of GL(N)." Thesis, 2020.

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In this paper, we prove the equality of the local arithmetic and analytic epsilon- and L-factors attached to the twisted exterior and symmetric square representations of GL(N). We will construct the twisted symmetric square local analytic gamma- and L-factor of GL(N) by applying Langlands-Shahidi method to odd GSpin groups. Then we reduce the problem to the stablity of local coefficients, and eventually prove the analytic stabitliy in this case by some analysis on the asymptotic behavior of certain partial Bessel functions.

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42

(10732485), Clinton W. Bradford. "Square Forms Factoring with Sieves." Thesis, 2021.

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Square Form Factoring is an <i>O</i>(<i>N</i><sup>1/4</sup>) factoring algorithm developed by D. Shanks using certain properties of quadratic forms. Central to the original algorithm is an iterative search for a square form. We propose a new subexponential-time algorithm called SQUFOF2, based on ideas of D. Shanks and R. de Vogelaire, which replaces the iterative search with a sieve, similar to the Quadratic Sieve.

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