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Relevant bibliographies by topics / Number theory – Elementary number theory – Primes

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Academic literature on the topic 'Number theory – Elementary number theory – Primes'

Author: Grafiati

Published: 4 June 2021

Last updated: 10 February 2022

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Journal articles on the topic "Number theory – Elementary number theory – Primes"

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Korniłowicz, Artur, and Dariusz Surowik. "Elementary Number Theory Problems. Part II." Formalized Mathematics 29, no. 1 (2021): 63–68. http://dx.doi.org/10.2478/forma-2021-0006.

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Summary In this paper problems 14, 15, 29, 30, 34, 78, 83, 97, and 116 from [6] are formalized, using the Mizar formalism [1], [2], [3]. Some properties related to the divisibility of prime numbers were proved. It has been shown that the equation of the form p 2 + 1 = q 2 + r 2, where p, q, r are prime numbers, has at least four solutions and it has been proved that at least five primes can be represented as the sum of two fourth powers of integers. We also proved that for at least one positive integer, the sum of the fourth powers of this number and its successor is a composite number. And fi

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Schinzel, A., and J. Wójcik. "On a problem in elementary number theory." Mathematical Proceedings of the Cambridge Philosophical Society 112, no. 2 (1992): 225–32. http://dx.doi.org/10.1017/s0305004100070912.

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Let ordq (a) be the exponent with which a prime q occurs in the factorization of a rational number a ≠ 0 and, if ordq (a) = 0, let Mq(a) be the multiplicative group generated by a modulo q. In the course of a group-theoretical investigation J. S. Wilson found he needed some results about integers a, b such that Mq(a) = Mq(b), indeed also for algebraic integers, and he proved some of what he needed. J. W. S. Cassels observed that Wilson's argument naturally proved the existence of infinitely many primes q with Mq(a) = Mq(b) for rational integers a, b with ab > 0, |a| > 1, |b| > 1. J. G

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Koukoulopoulos, Dimitris. "Pretentious multiplicative functions and the prime number theorem for arithmetic progressions." Compositio Mathematica 149, no. 7 (2013): 1129–49. http://dx.doi.org/10.1112/s0010437x12000802.

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AbstractBuilding on the concept ofpretentious multiplicative functions, we give a new and largely elementary proof of the best result known on the counting function of primes in arithmetic progressions.

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Voloch, José Felipe. "On a Question of Buium." Canadian Mathematical Bulletin 43, no. 2 (2000): 236–38. http://dx.doi.org/10.4153/cmb-2000-031-6.

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AbstractWe prove that , with p ranging over all primes, is independent of 1 over the integers, assuming a conjecture in elementary number theory generalizing the infinitude ofMersenne primes. This answers a question of Buium. We also prove a generalization.

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FARAG, HANY M. "DIRICHLET TRUNCATIONS OF THE RIEMANN ZETA FUNCTION IN THE CRITICAL STRIP POSSESS ZEROS NEAR EVERY VERTICAL LINE." International Journal of Number Theory 04, no. 04 (2008): 653–62. http://dx.doi.org/10.1142/s1793042108001596.

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We study the zeros of the finite truncations of the alternating Dirichlet series expansion of the Riemann zeta function in the critical strip. We do this with an (admittedly highly) ambitious goal in mind. Namely, that this series converges to the zeta function (up to a trivial term) in the critical strip and our hope is that if we can obtain good estimates for the zeros of these approximations it may be possible to generalize some of the results to zeta itself. This paper is a first step towards this goal. Our results show that these finite approximations have zeros near every vertical line (

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Cziszter, Kálmán. "The Noether number of p-groups." Journal of Algebra and Its Applications 18, no. 04 (2019): 1950066. http://dx.doi.org/10.1142/s021949881950066x.

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A group of order [Formula: see text] ([Formula: see text] prime) has an indecomposable polynomial invariant of degree at least [Formula: see text] if and only if the group has a cyclic subgroup of index at most [Formula: see text] or it is isomorphic to the elementary abelian group of order 8 or the Heisenberg group of order 27.

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Zazkis, Rina, and Stephen Campbell. "Divisibility and Multiplicative Structure of Natural Numbers: Preservice Teachers' Understanding." Journal for Research in Mathematics Education 27, no. 5 (1996): 540–63. http://dx.doi.org/10.5951/jresematheduc.27.5.0540.

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This study contributes to a growing body of research on teachers' content knowledge in mathematics. The domain under investigation was elementary number theory. Our main focus concerned the concept of divisibility and its relation to division, multiplication, prime and composite numbers, factorization, divisibility rules, and prime decomposition. We used a constructivist-oriented theoretical framework for analyzing and interpreting data acquired in clinical interviews with preservice teachers. Participants' responses to questions and tasks indicated pervasive dispositions toward procedural att

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Xu, Xingzhong. "Elementary abelian subgroups in some special 𝑝-groups". Journal of Group Theory 22, № 6 (2019): 1069–75. http://dx.doi.org/10.1515/jgth-2018-0193.

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Abstract Let P be a finite p-group and p an odd prime. Let {\mathcal{A}_{p}(P)_{\geq 2}} be a poset consisting of elementary abelian subgroups of rank at least 2. If the derived subgroup {P^{\prime}\cong C_{p}\times C_{p}} , then the spheres occurring in {\mathcal{A}_{p}(P)_{\geq 2}} all have the same dimension.

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KAWAUCHI, AKIO, and IKUO TAYAMA. "ENUMERATING PRIME LINKS BY A CANONICAL ORDER." Journal of Knot Theory and Its Ramifications 15, no. 02 (2006): 217–37. http://dx.doi.org/10.1142/s0218216506004439.

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The first author defined a well-order in the set of links by embedding it into a canonical well-ordered set of (integral) lattice points. He also gave elementary transformations among lattice points to enumerate the prime links in terms of lattice points under this order. In this paper, we add some new elementary transformations and explain how to enumerate the prime links. We show a table of the first 443 prime links arising from the lattice points of lengths up to 10 under this order. Our argument enables us to find 7 omissions and 1 overlap in Conway's table of prime links of 10 crossings.

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Jordan, Bruce W., and Yevgeny Zaytman. "On the bounded generation of arithmetic SL2." Proceedings of the National Academy of Sciences 116, no. 38 (2019): 18880–82. http://dx.doi.org/10.1073/pnas.1907728116.

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Let K be a number field and S be a finite set of primes of K containing the archimedean valuations. Let 𝒪 be the ring of S-integers in K. Morgan, Rapinchuck, and Sury [A. V. Morgan et al., Algebra Number Theory 12, 1949–1974 (2018)] have proved that if the group of units 𝒪× is infinite, then every matrix in SL2(𝒪) is a product of at most 9 elementary matrices. We prove that under the additional hypothesis that K has at least 1 real embedding or S contains a finite place we can get a product of at most 8 elementary matrices. If we assume a suitable generalized Riemann hypothesis, then every mat

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Dissertations / Theses on the topic "Number theory – Elementary number theory – Primes"

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Alazmi, Amal Abdullah. "The Prime Number Theorem: Elementary Results." Kent State University / OhioLINK, 2019. http://rave.ohiolink.edu/etdc/view?acc_num=kent1564916947385846.

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Chan, Ching-yin, and 陳靖然. "On k-tuples of almost primes." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hdl.handle.net/10722/195967.

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Olofsson, Rikard. "Problems in Number Theory related to Mathematical Physics." Doctoral thesis, Stockholm : Engineering sciences, Kungliga Tekniska högskolan, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-9514.

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Kong, Yafang, and 孔亚方. "On linear equations in primes and powers of two." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2013. http://hub.hku.hk/bib/B50533769.

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It is known that the binary Goldbach problem is one of the open problems on linear equations in primes, and it has the Goldbach-Linnik problem, that is, representation of an even integer in the form of two odd primes and powers of two, as its approximate problem. The theme of my research is on linear equations in primes and powers of two. Precisely, there are two cases: one pair of linear equations in primes and powers of two, and one class of pairs of linear equations in primes and powers of two, in this thesis. In 2002, D.R. Heath-Brown and P.C. Puchta obtained that every sufficiently lar

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Tringali, Salvatore. "Some questions in combinatorial and elementary number theory." Phd thesis, Université Jean Monnet - Saint-Etienne, 2013. http://tel.archives-ouvertes.fr/tel-01060871.

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This thesis is divided into two parts. Part I is about additive combinatorics. Part II deals with questions in elementary number theory. In Chapter 1, we generalize the Davenport transform to prove that if si S\mathbb A=(A, +)S is acancellative semigroup (either abelian or not) and SX, YS are non-empty subsets of SAS such that the subsemigroup generated by SYS is abelian, then SS|X+Y|\gc\min(\gamma(Y, |X|+|Y|-I)SS, where for SZ\subsetcq AS we let S\gamma(Z):=\sup_{z_0\in Z^\times}\in f_(z_0\nc z\inZ) (vm ord)(z-z_0)S. This implies an extension of Chowla's and Pillai's theorems for cyclic group

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Feldman, Ziv. "Describing pre-service teachers' developing understanding of elementary number of theory topics." Thesis, Boston University, 2012. https://hdl.handle.net/2144/12372.

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Thesis (Ed.D.)--Boston University PLEASE NOTE: Boston University Libraries did not receive an Authorization To Manage form for this thesis or dissertation. It is therefore not openly accessible, though it may be available by request. If you are the author or principal advisor of this work and would like to request open access for it, please contact us at open-help@bu.edu. Thank you.<br>Although elementary number theory topics are closely linked to foundational topics in number and operations and are prevalent in elementary and middle grades mathematics curricula, little is currently known abo

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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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Schlackow, Waldemar. "A sieve problem over the Gaussian integers." Thesis, University of Oxford, 2010. http://ora.ox.ac.uk/objects/uuid:b7d4ff88-1f93-41b4-9f81-055f8f1b1c51.

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Our main result is that there are infinitely many primes of the form a² + b² such that a² + 4b² has at most 5 prime factors. We prove this by first developing the theory of $L$-functions for Gaussian primes by using standard methods. We then give an exposition of the Siegel--Walfisz Theorem for Gaussian primes and a corresponding Prime Number Theorem for Gaussian Arithmetic Progressions. Finally, we prove the main result by using the developed theory together with Sieve Theory and specifically a weighted linear sieve result to bound the number of prime factors of a² + 4b². For the application

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Campbell, Stephen Roderick. "Preservice teachers' understanding of elementary number theory, qualitative constructivist research situated within a Kantian framework for understanding educational inquiry." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 1998. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp02/NQ37688.pdf.

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Carvalho, Leandro Rodrigues de [UNESP]. "O uso de elementos da criptografia como estímulo matemático na sala de aula." Universidade Estadual Paulista (UNESP), 2016. http://hdl.handle.net/11449/138879.

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Submitted by LEANDRO RODRIGUES DE CARVALHO null (leandrorodca@gmail.com) on 2016-05-20T19:48:46Z No. of bitstreams: 1 dissertacao-Leandro-profmat-2016.pdf: 1207301 bytes, checksum: 3605d67341c1a33446dc9c537f6b735e (MD5)<br>Rejected by Juliano Benedito Ferreira (julianoferreira@reitoria.unesp.br), reason: Foram realizadas suas submissões. Favor submeter novamente apenas uma vez com o arquivo correto. on 2016-05-24T14:34:08Z (GMT)<br>Submitted by LEANDRO RODRIGUES DE CARVALHO null (leandrorodca@gmail.com) on 2016-05-25T10:37:49Z No. of bitstreams: 1 dissertacao-Leandro-profmat-2016.pdf: 1207

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Books on the topic "Number theory – Elementary number theory – Primes"

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Stein, William. Elementary Number Theory: Primes, Congruences, and Secrets. Springer New York, 2009. http://dx.doi.org/10.1007/b13279.

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Elementary number theory: Primes, congruences, and secrets : a computational approach. Springer, 2009.

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A course in analytic number theory. American Mathematical Society, 2014.

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Florian, Luca, ed. Analytic number theory: Exploring the anatomy of integers. American Mathematical Society, 2012.

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Primes in number theory. Shaker, 2005.

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Strayer, James K. Elementary number theory. PWS Pub. Co, 1993.

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Landau, Edmund. Elementary number theory. 2nd ed. Chelsea Publishing, 1998.

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Jones, Gareth A. Elementary number theory. Springer, 1998.

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Elementary number theory. 2nd ed. Dover Publications, 2008.

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Elementary number theory. 6th ed. McGraw-Hill Higher Education, 2007.

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Book chapters on the topic "Number theory – Elementary number theory – Primes"

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Nathanson, Melvyn B. "Elementary estimates for primes." In Additive Number Theory. Springer New York, 1996. http://dx.doi.org/10.1007/978-1-4757-3845-2_6.

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Berrizbeitia, P., and P. D. T. A. Elliott. "On Products of Shifted Primes." In Analytic and Elementary Number Theory. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-4507-8_13.

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Effinger, Gove, and Gary L. Mullen. "Prime Numbers and Factorization." In Elementary Number Theory. Chapman and Hall/CRC, 2021. http://dx.doi.org/10.1201/9781003193111-2.

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Ono, Ken. "The Residue of p(N) Modulo Small Primes." In Analytic and Elementary Number Theory. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-4507-8_5.

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Goldfeld, D. "The Elementary Proof of the Prime Number Theorem: An Historical Perspective." In Number Theory. Springer New York, 2004. http://dx.doi.org/10.1007/978-1-4419-9060-0_10.

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Elliott, P. D. T. A. "Products of Shifted Primes. Multiplicative Analogues of Goldbach’s Problems, II." In Analytic and Elementary Number Theory. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-4507-8_12.

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Indlekofer, Karl-Heinz, and Nikolai M. Timofeev. "A Mean-Value Theorem for Multiplicative Functions on the Set of Shifted Primes." In Analytic and Elementary Number Theory. Springer US, 1998. http://dx.doi.org/10.1007/978-1-4757-4507-8_9.

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Fine, Benjamin, and Gerhard Rosenberger. "The Infinitude of Primes." In Number Theory. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43875-7_3.

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Fine, Benjamin, and Gerhard Rosenberger. "The Density of Primes." In Number Theory. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43875-7_4.

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Fine, Benjamin, and Gerhard Rosenberger. "Primes and Algebraic Number Theory." In Number Theory. Springer International Publishing, 2016. http://dx.doi.org/10.1007/978-3-319-43875-7_6.

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Conference papers on the topic "Number theory – Elementary number theory – Primes"

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CAI, TIANXIN, YONG ZHANG, and ZHONGYAN SHEN. "FIGURATE PRIMES AND HILBERT'S 8TH PROBLEM." In The 7th China–Japan Seminar on Number Theory. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814644938_0002.

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SUN, ZHI-WEI. "PROBLEMS ON COMBINATORIAL PROPERTIES OF PRIMES." In The 7th China–Japan Seminar on Number Theory. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814644938_0006.

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Ivanov, Konstantin S. "Theory of Continuously Variable Transmission With Two Degrees of Freedom: Paradox of Mechanics." In ASME 2012 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/imece2012-85762.

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Recently creation continuously variable transmission (CVT) having property of the adaptation to variable technological loading develops. Traditional CVT contains the hydraulic converter and gear differential with two degrees of freedom (patents of Crockett, Volkov). The hydraulic converter imposes differential constraint on movement of links of the mechanism with two degrees of freedom. It provides definability of movement of transmission. Take place progressive CVT without use of the hydraulic converter (Harries’s patent, Ivanov’s patent). Such transmission contains only gear differential wit

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Reports on the topic "Number theory – Elementary number theory – Primes"

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Rutherfoord, John, Doug Toussaint, and Ina Sarcevic. Closeout for U.S. Department of Energy Final Technical Report for University of Arizona grant DOE Award Number DE-FG03-95ER40906 From 1 February 1995 to 31 January 2004 Grant title: Theory and Phenomenology of Strong and Weak High Energy Physics (Task A) and Experimental Elementary Particle Physics (Task B). Office of Scientific and Technical Information (OSTI), 2005. http://dx.doi.org/10.2172/837330.

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