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Relevant bibliographies by topics / Curves, Algebraic. Functions, Abelian

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Dissertations / Theses
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Academic literature on the topic 'Curves, Algebraic. Functions, Abelian'

Author: Grafiati

Published: 4 June 2021

Last updated: 13 February 2022

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Journal articles on the topic "Curves, Algebraic. Functions, Abelian"

1

Eilbeck, J. C., M. England, and Y. Ônishi. "Abelian functions associated with genus three algebraic curves." LMS Journal of Computation and Mathematics 14 (November 1, 2011): 291–326. http://dx.doi.org/10.1112/s1461157010000355.

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AbstractWe develop the theory of Abelian functions associated with algebraic curves. The growth in computer power and the advancement of efficient symbolic computation techniques have allowed for recent progress in this area. In this paper we focus on the genus three cases, comparing the two canonical classes of hyperelliptic and trigonal curves. We present new addition formulae, derive bases for the spaces of Abelian functions and discuss the differential equations such functions satisfy.Supplementary materials are available with this article.

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Eilbeck, J. C., V. Z. Enolski, and J. Gibbons. "Sigma, tau and Abelian functions of algebraic curves." Journal of Physics A: Mathematical and Theoretical 43, no. 45 (2010): 455216. http://dx.doi.org/10.1088/1751-8113/43/45/455216.

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KOMEDA, JIRYO, SHIGEKI MATSUTANI, and EMMA PREVIATO. "THE SIGMA FUNCTION FOR WEIERSTRASS SEMIGROUPS 〈3, 7, 8〉 AND 〈6, 13, 14, 15, 16〉." International Journal of Mathematics 24, no. 11 (2013): 1350085. http://dx.doi.org/10.1142/s0129167x13500857.

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Compact Riemann surfaces and their abelian functions are instrumental to solve integrable equations; more recently the representation theory of the Monster and related modular forms have pointed to the relevance of τ-functions, which are in turn connected with a specific type of abelian function, the (Kleinian) σ-function. Klein originally generalized Weierstrass' σ-function to hyperelliptic curves in a geometric way, then from a modular point of view to trigonal curves. Recently a modular generalization for all curves was given, as well as the geometric one for certain affine planar curves, k

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4

Costello, Craig, Alyson Deines-Schartz, Kristin Lauter, and Tonghai Yang. "Constructing abelian surfaces for cryptography via Rosenhain invariants." LMS Journal of Computation and Mathematics 17, A (2014): 157–80. http://dx.doi.org/10.1112/s1461157014000370.

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AbstractThis paper presents an algorithm to construct cryptographically strong genus $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}2$ curves and their Kummer surfaces via Rosenhain invariants and related Kummer parameters. The most common version of the complex multiplication (CM) algorithm for constructing cryptographic curves in genus 2 relies on the well-studied Igusa invariants and Mestre’s algorithm for reconstructing the c

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5

LONG, LING, and JONATHAN D. H. SMITH. "Catalan loops." Mathematical Proceedings of the Cambridge Philosophical Society 149, no. 3 (2010): 445–53. http://dx.doi.org/10.1017/s0305004110000393.

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AbstractMotivated by a problem from number theory about the relationship between Fermat curves and modular curves, a new class of loops is introduced, the Catalan loops. In the number-theoretic context, these loops turn out to be abelian precisely when the Fermat curves and modular curves coincide. General Catalan loops arise on certain transversals to diagonal subgroups in special linear groups over rings with a topologically nilpotent element. The transversals consist of products of certain affine shears. In a Catalan loop, the multiplication and right division are given by rational function

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6

Everest, G. R., and Bríd Ní Fhlathúin. "The elliptic Mahler measure." Mathematical Proceedings of the Cambridge Philosophical Society 120, no. 1 (1996): 13–25. http://dx.doi.org/10.1017/s0305004100074624.

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In this paper, we are going to introduce an elliptic analogue of the classical Mahler measure of an integral polynomial. The measure is shown to vanish if and only if the roots of the polynomial are attached to division points of the curve. This is the exact analogue of the statement that the Mahler measure of an integral polynomial vanishes if and only if all of its roots are division points of the circle (in other words, roots of unity). The proof of this result exploits an integral representation for the local canonical heights on the elliptic curve. The integral is that of a simple polynom

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7

Binyamini, Gal. "Bezout-type theorems for differential fields." Compositio Mathematica 153, no. 4 (2017): 867–88. http://dx.doi.org/10.1112/s0010437x17007035.

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We prove analogs of the Bezout and the Bernstein–Kushnirenko–Khovanskii theorems for systems of algebraic differential conditions over differentially closed fields. Namely, given a system of algebraic conditions on the first $l$ derivatives of an $n$-tuple of functions, which admits finitely many solutions, we show that the number of solutions is bounded by an appropriate constant (depending singly-exponentially on $n$ and $l$) times the volume of the Newton polytope of the set of conditions. This improves a doubly-exponential estimate due to Hrushovski and Pillay. We illustrate the applicatio

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8

RICHARD, RODOLPHE. "RÉPARTITION GALOISIENNE D'UNE CLASSE D'ISOGÉNIE DE COURBES ELLIPTIQUES." International Journal of Number Theory 09, no. 02 (2012): 517–43. http://dx.doi.org/10.1142/s1793042112501199.

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Dans cet article, on montre que les orbites sous Galois des invariants modulaires associés à des courbes elliptiques complexes sans multiplication complexe variant dans une même classe d'isogénie s'équidistribuent dans la courbe modulaire vers la probabilité hyperbolique. La démonstration repose sur des arguments de théorie ergodique, notamment le théorème de Ratner (cf. [A. Eskin et H. Oh, Ergodic theoretic proof of equidistribution of Hecke points, Ergodic Theory Dynam. Systems26(1) (2006) 163–167]), ainsi que sur le théorème de l'image ouverte de Serre [J.-P. Serre, Abelian l-Adic Represent

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Lubicz, David, and Damien Robert. "Computing isogenies between abelian varieties." Compositio Mathematica 148, no. 5 (2012): 1483–515. http://dx.doi.org/10.1112/s0010437x12000243.

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AbstractWe describe an efficient algorithm for the computation of separable isogenies between abelian varieties represented in the coordinate system given by algebraic theta functions. Let A be an abelian variety of dimension g defined over a field of odd characteristic. Our algorithm comprises two principal steps. First, given a theta null point for A and a subgroup K isotropic for the Weil pairing, we explain how to compute the theta null point corresponding to the quotient abelian variety A/K. Then, from the knowledge of a theta null point of A/K, we present an algorithm to obtain a rationa

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10

LESFARI, A. "CYCLIC COVERINGS OF ABELIAN VARIETIES AND THE GENERALIZED YANG–MILLS SYSTEM FOR A FIELD WITH GAUGE GROUP SU(2)." International Journal of Geometric Methods in Modern Physics 05, no. 06 (2008): 947–61. http://dx.doi.org/10.1142/s0219887808003028.

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In this paper, we consider a dynamical system related to the Yang–Mills system for a field with gauge group SU(2). We solve this system in terms of genus two hyperelliptic functions. The corresponding invariant surface defined by the two constants of motion can be completed as a cyclic double cover of an abelian surface (the jacobian of a genus 2 curve) and we show that this system is algebraic completely integrable in the generalized sense. Also we show that this system is part of an algebraic completely integrable system in five unknowns having three constants of motion.

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Dissertations / Theses on the topic "Curves, Algebraic. Functions, Abelian"

1

England, Matthew. "Higher genus Abelian functions associated with algebraic curves." Thesis, Heriot-Watt University, 2009. http://hdl.handle.net/10399/2301.

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We investigate the theory of Abelian functions with periodicity properties defined from an associated algebraic curve. A thorough summary of the background material is given, including a synopsis of elliptic function theory, generalisations of the Weierstrass σ and 0functions and a literature review. The theory of Abelian functions associated with a tetragonal curve of genus six is considered in detail. Differential equations and addition formula satisfied by the functions are derived and a solution to the Jacobi Inversion Problem is presented. New methods which centre on a series expansion of

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Zeytin, Ayberk. "Algebraic Curves Hermitian Lattices And Hypergeometric Functions." Phd thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12613485/index.pdf.

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The aim of this work is to study the interaction between two classical objects of mathematics: the modular group, and the absolute Galois group. The latter acts on the category of finite index subgroups of the modular group. However, it is a task out of reach do understand this action in this generality. We propose a lattice which parametrizes a certain system of &rdquo<br>geometric&rdquo<br>elements in this category. This system is setwise invariant under the Galois action, and there is a hope that one can explicitly understand the pointwise action on the elements of this system. These elemen

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Dokchitser, Vladimir. "L-functions of non-abelian twists of elliptic curves." Thesis, University of Cambridge, 2005. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.615194.

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(topaloglu), Mete Pinar. "Hilbert Functions Of Gorenstein Monomial Curves." Phd thesis, METU, 2005. http://etd.lib.metu.edu.tr/upload/12606285/index.pdf.

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The aim of this thesis is to study the Hilbert function of a one-dimensional Gorenstein local ring of embedding dimension four in the case of monomial curves. We show that the Hilbert function is non-decreasing for some families of Gorenstein monomial curves in affine 4-space. In order to prove this result, under some arithmetic assumptions on generators of the defining ideal, we determine the minimal generators of their tangent cones by using the standard basis and check the Cohen-Macaulayness of them. Later, we determine the behavior of the Hilbert function of these curves, and we extend the

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Balister, P. N. "Two variable #rho#-adic L-functions for CM elliptic curves with supersingular reduction." Thesis, University of Cambridge, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.240890.

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Ducet, Virgile. "Construction of algebraic curves with many rational points over finite fields." Thesis, Aix-Marseille, 2013. http://www.theses.fr/2013AIXM4043/document.

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L'étude du nombre de points rationnels d'une courbe définie sur un corps fini se divise naturellement en deux cas : lorsque le genre est petit (typiquement g<=50), et lorsqu'il tend vers l'infini. Nous consacrons une partie de cette thèse à chacun de ces cas. Dans la première partie de notre étude nous expliquons comment calculer l'équation de n'importe quel revêtement abélien d'une courbe définie sur un corps fini. Nous utilisons pour cela la théorie explicite du corps de classe fournie par les extensions de Kummer et d'Artin-Schreier-Witt. Nous détaillons également un algorithme pour la r

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Helminck, Paul Alexander [Verfasser], Eva-Maria [Akademischer Betreuer] Feichtner, Eva-Maria [Gutachter] Feichtner, and Joseph [Gutachter] Rabinoff. "Tropicalizing abelian covers of algebraic curves / Paul Alexander Helminck ; Gutachter: Eva-Maria Feichtner, Joseph Rabinoff ; Betreuer: Eva-Maria Feichtner." Bremen : Staats- und Universitätsbibliothek Bremen, 2018. http://d-nb.info/1163012882/34.

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Agostini, Daniele. "On syzygies of algebraic varieties with applications to moduli." Doctoral thesis, Humboldt-Universität zu Berlin, 2018. http://dx.doi.org/10.18452/19415.

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Diese Dissertation beschäftigt sich mit asymptotischen Syzygien und Gleichungen Abelscher Varietäten, sowie mit deren Anwendung auf zyklische Überdeckungen von Kurven von Geschlecht zwei. Was asymptotischen Syzygien angeht, zeigen wir für beliebige Geradenbündel auf projektiven Schemata: Wenn die asymptotischen Syzygien von Grad p eines Geradenbündels verschwinden, dann ist das Geradenbündel p-sehr ampel. Darüber hinaus verwenden wir die Bridgeland-King-Reid-Haiman Korrespondenz, um zu zeigen, dass dieses Ergebnis auch umgekehrt wahr ist, wenn es um eine glatte Fläche und kleine p geht. D

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Frejlich, Pedro. "Transformada de Nahm de fibrados de Higgs sobre superficies de Riemann de genero ao menos dois." [s.n.], 2006. http://repositorio.unicamp.br/jspui/handle/REPOSIP/306023.

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Orientador: Marcos Benevuto Jardim<br>Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica<br>Made available in DSpace on 2018-08-08T04:40:41Z (GMT). No. of bitstreams: 1 Frejlich_Pedro_M.pdf: 852390 bytes, checksum: bcde0cd89c0bcfe3b2515b5cfe48e528 (MD5) Previous issue date: 2007<br>Resumo: Construímos a transformada de Nahm de um fibrado de Higgs estável de grau nulo sobre uma superfície de Riemann de gênero pelo menos 2. Para tanto, empregamos a Teoria do Índice de Atiyah-Singer e um vanishing theorem que segue da hipótes

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Killian, Kenneth. "Maxwell’s Problem on Point Charges in the Plane." Scholar Commons, 2008. https://scholarcommons.usf.edu/etd/333.

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This paper deals with approximating an upper bound for the number of equilibrium points of a potential field produced by point charges in the plane. This is a simplified form of a problem posed by Maxwell [4], who considered spatial configurations of the point charges. Using algebraic techniques, we will give an upper bound for planar charges that is sharper than the bound given in [6] for most general configurations of charges. Then we will study an example of a configuration of charges that has exactly the number of equilibrium points that Maxwell's conjecture predicts, and we will look into

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Books on the topic "Curves, Algebraic. Functions, Abelian"

1

Cremona, John E. Modular Curves and Abelian Varieties. Birkhäuser Basel, 2004.

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2

Lang, Serge. Introduction to algebraic and abelian functions. 2nd ed. Springer-Verlag, 1995.

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3

Shparlinski, Igor E., and David R. Kohel. Frobenius distributions: Lang-Trotter and Sato-Tate conjectures : Winter School on Frobenius Distributions on Curves, February 17-21, 2014 [and] Workshop on Frobenius Distributions on Curves, February 24-28, 2014, Centre International de Rencontres Mathematiques, Marseille, France. American Mathematical Society, 2016.

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4

Algebraic functions and projective curves. Springer, 2003.

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5

Goldschmidt, David M. Algebraic Functions and Projective Curves. Springer New York, 2003. http://dx.doi.org/10.1007/b97844.

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6

Yang, Kichoon. Meromorphic functions and projective curves. Kluwer Academic Publishers, 1999.

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7

Win-- women in numbers: Research directions in number theory. American Mathematical Society, 2011.

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8

Moreno, Carlos J. Algebraic curves over finite fields. Cambridge University Press, 1991.

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9

1965-, Aubry Yves, Ritzenthaler Christophe 1976-, Zykin Alexey 1984-, and Geocrypt Conference (2011 : Bastia, France), eds. Arithmetic, geometry, cryptography and coding theory: 13th Conference on Arithmetic, Geometry, Cryptography and Coding Theory, March 14-18, 2011, CIRM, Marseille, France : Geocrypt 2011, June 19-24, 2011, Bastia, France. American Mathematical Society, 2012.

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Rodríguez, Rubí E., 1953- editor of compilation, ed. Riemann and Klein surfaces, automorphisms, symmetries and moduli spaces: Conference in honor of Emilio Bujalance on Riemann and Klein surfaces, symmetries and moduli spaces, June 24-28, 2013, Linköping University, Linköping, Sweden. American Mathematical Society, 2014.

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Book chapters on the topic "Curves, Algebraic. Functions, Abelian"

1

Eilbeck, J., V. Enolskii, and D. Leykin. "On the Kleinian construction of abelian functions of canonical algebraic curves." In SIDE III—Symmetries and Integrability of Difference Equations. American Mathematical Society, 2000. http://dx.doi.org/10.1090/crmp/025/12.

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Goldschmidt, David M. "Projective Curves." In Algebraic Functions and Projective Curves. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-22445-9_4.

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Goldschmidt, David M. "Zeta Functions." In Algebraic Functions and Projective Curves. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-22445-9_5.

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Beals, Richard, and Roderick S. C. Wong. "Riemann surfaces and algebraic curves." In Explorations in Complex Functions. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-54533-8_7.

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Yang, Kichoon. "Analytic and Algebraic Families." In Meromorphic Functions and Projective Curves. Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-015-9151-5_2.

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Wang, Ren-Hong. "Piecewise algebraic curves and surfaces." In Multivariate Spline Functions and Their Applications. Springer Netherlands, 2001. http://dx.doi.org/10.1007/978-94-017-2378-7_6.

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Goldschmidt, David M. "Function Fields." In Algebraic Functions and Projective Curves. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-22445-9_2.

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Goldschmidt, David M. "Finite Extensions." In Algebraic Functions and Projective Curves. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-22445-9_3.

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Goldschmidt, David M. "Background." In Algebraic Functions and Projective Curves. Springer New York, 2003. http://dx.doi.org/10.1007/0-387-22445-9_1.

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Manin, Yu I. "Generating Functions in Algebraic Geometry and Sums Over Trees." In The Moduli Space of Curves. Birkhäuser Boston, 1995. http://dx.doi.org/10.1007/978-1-4612-4264-2_14.

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Conference papers on the topic "Curves, Algebraic. Functions, Abelian"

1

WENG, Lin. "Refined Brill-Noether Locus and Non-Abelian Zeta Functions for Elliptic Curves." In Proceedings of the Symposium. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812705105_0011.

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CAUBERGH, M., and F. DUMORTIER. "THE USE OF MELNIKOV FUNCTIONS IN MULTI-DIMENSIONAL PARAMETER FAMILIES: ALGEBRAIC CURVES OF MAXIMAL CYCLICITY." In Proceedings of the International Conference on Differential Equations. WORLD SCIENTIFIC, 2005. http://dx.doi.org/10.1142/9789812702067_0047.

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Blechschmidt, James L., and Chung-Hsing Lee. "The Design and Analysis of Cam Profiles Using Algebraic Functions." In ASME 1991 Design Technical Conferences. American Society of Mechanical Engineers, 1991. http://dx.doi.org/10.1115/detc1991-0150.

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Abstract A new method for the design and analysis of cam profiles is developed and demonstrated in this paper using algebraic functions in two variables. A technique for the construction of the cam profile directly without using the lift curve is developed. The basis for this analysis is the use of Boolean operators in algebra using a form of algebraic function called the defining function. Using simple quadratic curves such as circles, ellipses, and slabs, more complicated cam profiles are constructed using the Boolean operators of union, intersection, and difference. The resulting closed alg

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4

Ganter, M. A., and D. W. Storti. "Object Extent Determination for Algebraic Solid Models." In ASME 1992 Design Technical Conferences. American Society of Mechanical Engineers, 1992. http://dx.doi.org/10.1115/detc1992-0176.

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Abstract This paper presents methods for determination of spatial extent of algebraic solid models. Algebraic solid models (ASM) are a variation of implicit solid models defined by implicit polynomial functions with rational coefficients. Spatial extent information, which can be used to enhance the performance of visualization and property evaluation, includes silhouettes, outlines and profiles. Silhouettes are curves on the surface of the solid which separate portions of the surface which face towards or away from a given viewpoint. The projection of the silhouette onto the viewing plane give

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Venkataraman, P. "One and Two Dimensional Data Analysis Using Bezier Functions." In ASME 2008 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2008. http://dx.doi.org/10.1115/detc2008-49101.

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Bezier functions, which are Bezier curves constrained to behave like functions, are excellent for representing smooth and continuous function of high degree, over the entire range of the independent variable. They provide excellent solutions to systems of linear, nonlinear, ordinary and partial differential equations. In this paper we examine their usefulness for data approximation as a prelude to their use in solving the inverse problem. Bezier function and B-splines, which are related, have mostly been used in geometrical modeling. There are not many examples of their use in data analysis. I

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Krack, Malte, Lars Panning-von Scheidt, Jörg Wallaschek, Christian Siewert, and Andreas Hartung. "Reduced Order Modeling Based on Complex Nonlinear Modal Analysis and its Application to Bladed Disks With Shroud Contact." In ASME Turbo Expo 2013: Turbine Technical Conference and Exposition. American Society of Mechanical Engineers, 2013. http://dx.doi.org/10.1115/gt2013-94560.

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The design of bladed disks with contact interfaces typically requires analyses of the resonant forced response and flutter-induced limit cycle oscillations. The steady-state vibration behavior can efficiently be calculated using the Multi-Harmonic Balance method. The dimension of the arising algebraic systems of equations is essentially proportional to the number of harmonics and the number of degrees of freedom (DOFs) retained in the model. Extensive parametric studies necessary e.g. for robust design optimization are often not possible in practice due to the resulting computational effort. I

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