Log in

Relevant bibliographies by topics / Number theory – Multiplicative number theory – Primes in progressions / Journal articles

To see the other types of publications on this topic, follow the link: Number theory – Multiplicative number theory – Primes in progressions.

Journal articles on the topic 'Number theory – Multiplicative number theory – Primes in progressions'

Author: Grafiati

Published: 4 June 2021

Last updated: 28 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Number theory – Multiplicative number theory – Primes in progressions.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

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.

Full text

Abstract:

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.

APA, Harvard, Vancouver, ISO, and other styles

2

Granville, Andrew, Adam J. Harper, and K. Soundararajan. "A new proof of Halász’s theorem, and its consequences." Compositio Mathematica 155, no. 1 (2018): 126–63. http://dx.doi.org/10.1112/s0010437x18007522.

Full text

Abstract:

Halász’s theorem gives an upper bound for the mean value of a multiplicative function$f$. The bound is sharp for general such$f$, and, in particular, it implies that a multiplicative function with$|f(n)|\leqslant 1$has either mean value$0$, or is ‘close to’$n^{it}$for some fixed$t$. The proofs in the current literature have certain features that are difficult to motivate and which are not particularly flexible. In this article we supply a different, more flexible, proof, which indicates how one might obtain asymptotics, and can be modified to treat short intervals and arithmetic progressions.

APA, Harvard, Vancouver, ISO, and other styles

3

Hammonds, Trajan, Casimir Kothari, Noah Luntzlara, Steven J. Miller, Jesse Thorner, and Hunter Wieman. "The explicit Sato–Tate conjecture for primes in arithmetic progressions." International Journal of Number Theory 17, no. 08 (2021): 1905–23. http://dx.doi.org/10.1142/s179304212150069x.

Full text

Abstract:

Let [Formula: see text] be Ramanujan’s tau function, defined by the discriminant modular form [Formula: see text] (this is the unique holomorphic normalized cuspidal newform of weight 12 and level 1). Lehmer’s conjecture asserts that [Formula: see text] for all [Formula: see text]; since [Formula: see text] is multiplicative, it suffices to study primes [Formula: see text] for which [Formula: see text] might possibly be zero. Assuming standard conjectures for the twisted symmetric power [Formula: see text]-functions associated to [Formula: see text] (including GRH), we prove that if [Formula:

APA, Harvard, Vancouver, ISO, and other styles

4

Grabowski, Adam. "Elementary Number Theory Problems. Part XII – Primes in Arithmetic Progression." Formalized Mathematics 31, no. 1 (2023): 277–86. http://dx.doi.org/10.2478/forma-2023-0022.

Full text

Abstract:

Summary In this paper another twelve problems from W. Sierpiński’s book “250 Problems in Elementary Number Theory” are formalized, using the Mizar formalism, namely: 42, 43, 51, 51a, 57, 59, 72, 135, 136, and 153–155. Significant amount of the work is devoted to arithmetic progressions.

APA, Harvard, Vancouver, ISO, and other styles

5

Puchta, Jan-Christoph. "Primes in short arithmetic progressions." Acta Arithmetica 106, no. 2 (2003): 143–49. http://dx.doi.org/10.4064/aa106-2-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

6

BAIER, STEPHAN, and LIANGYI ZHAO. "ON PRIMES IN QUADRATIC PROGRESSIONS." International Journal of Number Theory 05, no. 06 (2009): 1017–35. http://dx.doi.org/10.1142/s1793042109002523.

Full text

APA, Harvard, Vancouver, ISO, and other styles

7

Wójcik, J. "On a problem in algebraic number theory." Mathematical Proceedings of the Cambridge Philosophical Society 119, no. 2 (1996): 191–200. http://dx.doi.org/10.1017/s0305004100074090.

Full text

Abstract:

Let K be an algebraic number field. If q is a prime ideal of the ring of integers of K and α is a number of K prime to q then Mq(α) denotes the multiplicative group generated by α modulo q. In the paper [5] there is the remark: ‘We do not know whether for all a, b, c ∈ ℚ with abc ≠ 0, |a| ≠ 1,|b| ≠ 1,|c| ≠ 1 there exist infinitely many primes q with Mq (a) = Mq (b) = Mq (c).’

APA, Harvard, Vancouver, ISO, and other styles

8

Ramaré, Olivier, Priyamvad Srivastav, and Oriol Serra. "Product of primes in arithmetic progressions." International Journal of Number Theory 16, no. 04 (2019): 747–66. http://dx.doi.org/10.1142/s1793042120500384.

Full text

Abstract:

We prove that, for all [Formula: see text] and for all invertible residue classes [Formula: see text] modulo [Formula: see text], there exists a natural number [Formula: see text] that is congruent to [Formula: see text] modulo [Formula: see text] and that is the product of exactly three primes, all of which are below [Formula: see text]. The proof is further supplemented with a self-contained proof of the special case of the Kneser Theorem we use.

APA, Harvard, Vancouver, ISO, and other styles

9

Dudek, Adrian W., Loïc Grenié, and Giuseppe Molteni. "Explicit short intervals for primes in arithmetic progressions on GRH." International Journal of Number Theory 15, no. 04 (2019): 825–62. http://dx.doi.org/10.1142/s1793042119500441.

Full text

APA, Harvard, Vancouver, ISO, and other styles

10

TANNER, NOAM. "STRINGS OF CONSECUTIVE PRIMES IN FUNCTION FIELDS." International Journal of Number Theory 05, no. 01 (2009): 81–88. http://dx.doi.org/10.1142/s1793042109001918.

Full text

Abstract:

In a recent paper, Thorne [5] proved the existence of arbitrarily long strings of consecutive primes in arithmetic progressions in the polynomial ring 𝔽q[t]. Here we extend this result to show that given any k there exists a string of k consecutive primes of degree D in arithmetic progression for all sufficiently large D.

APA, Harvard, Vancouver, ISO, and other styles

11

Debaene, Korneel. "Explicit counting of ideals and a Brun–Titchmarsh inequality for the Chebotarev density theorem." International Journal of Number Theory 15, no. 05 (2019): 883–905. http://dx.doi.org/10.1142/s1793042119500477.

Full text

Abstract:

We prove a bound on the number of primes with a given splitting behavior in a given field extension. This bound generalizes the Brun–Titchmarsh bound on the number of primes in an arithmetic progression. The proof is set up as an application of Selberg’s Sieve in number fields. The main new ingredient is an explicit counting result estimating the number of integral elements with certain properties up to multiplication by units. As a consequence of this result, we deduce an explicit estimate for the number of ideals of norm up to [Formula: see text].

APA, Harvard, Vancouver, ISO, and other styles

12

Zhou, Binbin. "The Chen primes contain arbitrarily long arithmetic progressions." Acta Arithmetica 138, no. 4 (2009): 301–15. http://dx.doi.org/10.4064/aa138-4-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

13

Park, Poo-Sung. "Additive uniqueness of PRIMES − 1 for multiplicative functions." International Journal of Number Theory 16, no. 06 (2020): 1369–76. http://dx.doi.org/10.1142/s1793042120500724.

Full text

Abstract:

Let [Formula: see text] be the set of all primes. A function [Formula: see text] is called multiplicative if [Formula: see text] and [Formula: see text] when [Formula: see text]. We show that a multiplicative function [Formula: see text] which satisfies [Formula: see text] satisfies one of the following: (1) [Formula: see text] is the identity function, (2) [Formula: see text] is the constant function with [Formula: see text], (3) [Formula: see text] for [Formula: see text] unless [Formula: see text] is odd and squareful. As a consequence, a multiplicative function which satisfies [Formula: se

APA, Harvard, Vancouver, ISO, and other styles

14

RIBENBOIM, PAULO. "MULTIPLE PATTERNS OF k-TUPLES OF INTEGERS." International Journal of Number Theory 07, no. 07 (2011): 1761–79. http://dx.doi.org/10.1142/s1793042111004733.

Full text

Abstract:

The first proposition and its corollary are a transfiguration of Dirichlet's pigeon-hole principle. They are applied to show that a wide variety of sequences display arbitrarily large patterns of sums, differences, higher differences, etc. Among these, we include sequences of primes in arithmetic progressions, of powerful integers, sequences of integers with radical index having a prescribed lower bound, and many others. We also deal with patterns in iterated sequences of primes, patterns of gaps between primes, patterns of values of Euler's φ-function, or their gaps, as well as patterns relat

APA, Harvard, Vancouver, ISO, and other styles

15

KNAFO, EMMANUEL. "EFFECTIVE LOWER BOUND FOR THE VARIANCE OF DISTRIBUTION OF PRIMES IN ARITHMETIC PROGRESSIONS." International Journal of Number Theory 04, no. 01 (2008): 45–56. http://dx.doi.org/10.1142/s1793042108001213.

Full text

Abstract:

Through a refinement for the estimation of the effect of Siegel zeros, we show how to avoid the use of Siegel's theorem in order to obtain the first effective lower bound for the variance of distribution of primes in arithmetic progressions.

APA, Harvard, Vancouver, ISO, and other styles

16

Saradha, N., and R. Tijdeman. "Arithmetic progressions with common difference divisible by small primes." Acta Arithmetica 131, no. 3 (2008): 267–79. http://dx.doi.org/10.4064/aa131-3-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

17

Elliott, P. D. T. A. "Multiplicative Functions on Arithmetic Progressions. VI. More Middle Moduli." Journal of Number Theory 44, no. 2 (1993): 178–208. http://dx.doi.org/10.1006/jnth.1993.1044.

Full text

APA, Harvard, Vancouver, ISO, and other styles

18

Bachman, Gennady. "Some Remarks on Nonnegative Multiplicative Functions on Arithmetic Progressions." Journal of Number Theory 73, no. 1 (1998): 72–91. http://dx.doi.org/10.1006/jnth.1998.2279.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Elliott, P. D. T. A. "Primes in progressions to moduli with a large power factor." Ramanujan Journal 13, no. 1-3 (2007): 241–51. http://dx.doi.org/10.1007/s11139-006-0250-4.

Full text

APA, Harvard, Vancouver, ISO, and other styles

20

Elliott, P. "Products of shifted primes: Multiplicative analogues of Goldbach's problem." Acta Arithmetica 88, no. 1 (1999): 31–50. http://dx.doi.org/10.4064/aa-88-1-31-50.

Full text

APA, Harvard, Vancouver, ISO, and other styles

21

Chirre, Andrés, Valdir Pereira Júnior, and David de Laat. "Primes in arithmetic progressions and semidefinite programming." Mathematics of Computation 90, no. 331 (2021): 2235–46. http://dx.doi.org/10.1090/mcom/3638.

Full text

Abstract:

Assuming the generalized Riemann hypothesis, we give asymptotic bounds on the size of intervals that contain primes from a given arithmetic progression using the approach developed by Carneiro, Milinovich and Soundararajan [Comment. Math. Helv. 94, no. 3 (2019)]. For this we extend the Guinand-Weil explicit formula over all Dirichlet characters modulo q ≥ 3 q \geq 3 , and we reduce the associated extremal problems to convex optimization problems that can be solved numerically via semidefinite programming.

APA, Harvard, Vancouver, ISO, and other styles

22

Ramaré, Olivier, and Aled Walker. "Products of primes in arithmetic progressions: a footnote in parity breaking." Journal de Théorie des Nombres de Bordeaux 30, no. 1 (2018): 219–25. http://dx.doi.org/10.5802/jtnb.1024.

Full text

APA, Harvard, Vancouver, ISO, and other styles

23

Halupczok, Karin. "Goldbach’s problem with primes in arithmetic progressions and in short intervals." Journal de Théorie des Nombres de Bordeaux 25, no. 2 (2013): 331–51. http://dx.doi.org/10.5802/jtnb.839.

Full text

APA, Harvard, Vancouver, ISO, and other styles

24

Aaccagnini, Alessandro. "A note on large gaps between consecutive primes in arithmetic progressions." Journal of Number Theory 42, no. 1 (1992): 100–102. http://dx.doi.org/10.1016/0022-314x(92)90111-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

25

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.

Full text

Abstract:

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

APA, Harvard, Vancouver, ISO, and other styles

26

Bauer, Claus, and Yonghui Wang. "The binary Goldbach conjecture with primes in arithmetic progressions with large modulus." Acta Arithmetica 159, no. 3 (2013): 227–43. http://dx.doi.org/10.4064/aa159-3-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

27

Dudek, Adrian W., and David J. Platt. "On the sum of the square of a prime and a square-free number." LMS Journal of Computation and Mathematics 19, no. 1 (2016): 16–24. http://dx.doi.org/10.1112/s1461157015000297.

Full text

Abstract:

We prove that every integer$n\geqslant 10$such that$n\not \equiv 1\text{ mod }4$can be written as the sum of the square of a prime and a square-free number. This makes explicit a theorem of Erdős that every sufficiently large integer of this type may be written in such a way. Our proof requires us to construct new explicit results for primes in arithmetic progressions. As such, we use the second author’s numerical computation regarding the generalised Riemann hypothesis to extend the explicit bounds of Ramaré–Rumely.

APA, Harvard, Vancouver, ISO, and other styles

28

Maier, Helmut, and Saurabh Kumar Singh. "On multiplicative functions with mean-value close to −1 on primes." Journal of Number Theory 197 (April 2019): 89–105. http://dx.doi.org/10.1016/j.jnt.2018.08.001.

Full text

APA, Harvard, Vancouver, ISO, and other styles

29

Valluri, Maheswara Rao. "A quantum algorithm for computing multiplicative order of integers modulo a prime." Journal of Discrete Mathematical Sciences & Cryptography 26, no. 2 (2023): 573–84. http://dx.doi.org/10.47974/jdmsc-1557.

Full text

Abstract:

One of the challenging problems in number theory is to compute efficiently multiplicative order of integers modulo a prime. This problem was listed under open problems in the number theoretic complexity II proposed by Leonard M. Adleman and Kevin S.McCurley in 1994. This paper offers a polynomial-time quantum algorithm for computing the order k = min {x|x∈, ax ≡ 1(modp)}, if p∈ Primes and gcd(a,p) = 1, where a, p∈, and it requires 2 (1) 2 ((log p) +O )  quantum operations.

APA, Harvard, Vancouver, ISO, and other styles

30

Pritchard, Paul A. "Long arithmetic progressions of primes: some old, some new." Mathematics of Computation 45, no. 171 (1985): 263. http://dx.doi.org/10.1090/s0025-5718-1985-0790659-1.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Guiasu, Silviu. "Detecting a Regularity in the Generation and Utilization of Primes in the Multiplicative Number Theory." Natural Science 11, no. 06 (2019): 187–96. http://dx.doi.org/10.4236/ns.2019.116019.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Halupczok, Karin. "On the ternary Goldbach problem with primes in arithmetic progressions having a common modulus." Journal de Théorie des Nombres de Bordeaux 21, no. 1 (2009): 203–13. http://dx.doi.org/10.5802/jtnb.666.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Yau, Kam Hung. "On products of primes and square-free integers in arithmetic progressions." New Zealand Journal of Mathematics 50 (November 14, 2020): 93–99. http://dx.doi.org/10.53733/66.

Full text

Abstract:

We obtain an asymptotic formula for the number of ways to represent every reduced residue class as a product of a prime and square-free integer. This may be considered as a relaxed version of a conjecture of Erd\"os, Odlyzko, and S\'ark\"ozy.

APA, Harvard, Vancouver, ISO, and other styles

34

LUCA, FLORIAN, and YOHEI TACHIYA. "IRRATIONALITY OF LAMBERT SERIES ASSOCIATED WITH A PERIODIC SEQUENCE." International Journal of Number Theory 10, no. 03 (2014): 623–36. http://dx.doi.org/10.1142/s1793042113501121.

Full text

Abstract:

Let q be an integer with |q| > 1 and {an}n≥1 be an eventually periodic sequence of rational numbers, not identically zero from some point on. Then the number [Formula: see text] is irrational. In particular, if the periodic sequences [Formula: see text] of rational numbers are linearly independent over ℚ, then so are the following m + 1 numbers: [Formula: see text] This generalizes a result of Erdős who treated the case of m = 1 and [Formula: see text]. The method of proof is based on the original approaches of Chowla and Erdős, together with some results about primes in arithmetic progress

APA, Harvard, Vancouver, ISO, and other styles

35

Hall, R. R., and G. Tenenbaum. "Effective mean value estimates for complex multiplicative functions." Mathematical Proceedings of the Cambridge Philosophical Society 110, no. 2 (1991): 337–51. http://dx.doi.org/10.1017/s0305004100070419.

Full text

Abstract:

Quantitative estimates for finite mean valuesof multiplicative functions are highly applicable tools in analytic and probabilistic number theory. Extending a result of Hall [4], Halberstam and Richert[3] proved a useful inequality valid for real, non-negative g satisfying for instance a Wirsing type condition, viz for all primes p, with constants λ1 ≥ 0, 0 ≤ λ2 < 2. Their upper bound is sharp to within a factor (l + o(l)), but even a weaker and easier to prove estimate, such as(where the implied constants depend on λ1 and λ2), may become a surprisingly strong device. For instance, setting g

APA, Harvard, Vancouver, ISO, and other styles

36

Ting, John Y. C. "On the Universal Presence of Mathematics for Incompletely Predictable Problems in Rigorous Proofs for Riemann Hypothesis, Modified Polignac’s and Twin Prime Conjectures." Journal of Mathematics Research 16, no. 2 (2024): 1. http://dx.doi.org/10.5539/jmr.v16n2p1.

Full text

Abstract:

We validly ignore even prime number 2. Based on all arbitrarily large number of even Prime gaps 2, 4, 6, 8, 10...; the complete set and its derived subsets of Odd Primes fully comply with the Prime number theorem for Arithmetic Progressions, and our derived Generic Squeeze theorem and Theorem of Divergent-to-Convergent series conversion for Prime numbers. With these conditions being satisfied by all Odd Primes, we argue Polignac&#39;s and Twin prime conjectures are proven to be true when they are usefully treated as Incompletely Predictable Problems. In so doing [and with Riemann hypothesi

APA, Harvard, Vancouver, ISO, and other styles

37

Heboub, Lakhdar, and Douadi Mihoubi. "Minimal and maximal cyclic codes of length 2p." Journal of Discrete Mathematical Sciences & Cryptography 27, no. 1 (2024): 63–74. http://dx.doi.org/10.47974/jdmsc-1569.

Full text

Abstract:

In this paper, we compute the maximal and minimal codes of length 2p over finite fields Fq with p and q are distinct odd primes and f(p) = p – 1 is the multiplicative order of q modulo 2p. We show that, every cyclic code is a direct sum of minimal cyclic codes.

APA, Harvard, Vancouver, ISO, and other styles

38

Lebowitz-Lockard, Noah. "Additively unique sets of prime numbers." International Journal of Number Theory 14, no. 10 (2018): 2757–65. http://dx.doi.org/10.1142/s179304211850166x.

Full text

Abstract:

Spiro proved that the identity function is the only multiplicative function with [Formula: see text] for some prime [Formula: see text] and [Formula: see text] for all prime [Formula: see text] and [Formula: see text]. We determine the sets [Formula: see text] of primes for which restricting our condition to [Formula: see text] for all [Formula: see text] still implies that [Formula: see text] is the identity function. We prove that [Formula: see text] satisfies these conditions if and only if [Formula: see text] contains every prime that is not the larger element of a twin prime pair and [For

APA, Harvard, Vancouver, ISO, and other styles

39

SMILANSKY, YOTAM. "SUMS OF TWO SQUARES — PAIR CORRELATION AND DISTRIBUTION IN SHORT INTERVALS." International Journal of Number Theory 09, no. 07 (2013): 1687–711. http://dx.doi.org/10.1142/s1793042113500516.

Full text

Abstract:

In this work we show that based on a conjecture for the pair correlation of integers representable as sums of two squares, which was first suggested by Connors and Keating and reformulated here, the second moment of the distribution of the number of representable integers in short intervals is consistent with a Poisson distribution, where "short" means of length comparable to the mean spacing between sums of two squares. In addition we present a method for producing such conjectures through calculations in prime power residue rings and describe how these conjectures, as well as the above state

APA, Harvard, Vancouver, ISO, and other styles

40

Hudson, Richard H. "Averaging effects on irregularities in the distribution of primes in arithmetic progressions." Mathematics of Computation 44, no. 170 (1985): 561. http://dx.doi.org/10.1090/s0025-5718-1985-0777286-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

41

KACZOROWSKI, J., and A. PERELLI. "On the distribution in short intervals of products of a prime and integers from a given set." Mathematical Proceedings of the Cambridge Philosophical Society 124, no. 1 (1998): 1–14. http://dx.doi.org/10.1017/s0305004197002284.

Full text

Abstract:

A classical problem in analytic number theory is the distribution in short intervals of integers with a prescribed multiplicative structure, such as primes, almost-primes, k-free numbers and others. Recently, partly due to applications to cryptology, much attention has been received by the problem of the distribution in short intervals of integers without large prime factors, see Lenstra–Pila–Pomerance [3] and section 5 of the excellent survey by Hildebrand–Tenenbaum [1].In this paper we deal with the distribution in short intervals of numbers representable as a product of a prime and integers

APA, Harvard, Vancouver, ISO, and other styles

42

Kadiri, H. "Short effective intervals containing primes in arithmetic progressions and the seven cubes problem." Mathematics of Computation 77, no. 263 (2008): 1733–48. http://dx.doi.org/10.1090/s0025-5718-08-02084-x.

Full text

APA, Harvard, Vancouver, ISO, and other styles

43

Győry, K., L. Hajdu, and A. Sárközy. "On additive and multiplicative decompositions of sets of integers composed from a given set of primes, I (Additive decompositions)." Acta Arithmetica 202, no. 1 (2022): 29–42. http://dx.doi.org/10.4064/aa210309-14-6.

Full text

APA, Harvard, Vancouver, ISO, and other styles

44

Balonin, Nikolay, and Mikhail Sergeev. "Odin and Shadow Cretan matrices accompanying primes and their powers." Information and Control Systems, no. 1 (March 2, 2022): 2–7. http://dx.doi.org/10.31799/1684-8853-2022-1-2-7.

Full text

Abstract:

Introduction: Cretan matrices – orthogonal matrices, consisting of the elements 1 and –b (real number), are an ideal object for the visual application of finite-dimensional mathematics. These matrices include, in particular, the Hadamard matrices and, with the expansion of the number of elements, the conference matrices. The most convenient research apparatus is to use field theory and multiplicative Galois groups, which is especially important for new types of Cretan matrices. Purpose: To study the symmetries of the Cretan matrices and to investigate two new types of matrices of odd and even

APA, Harvard, Vancouver, ISO, and other styles

45

Koshkin, Sergiy, and Jaeho Lee. "Panmagic Permutations and N-ary Groups." PUMP Journal of Undergraduate Research 8 (May 13, 2025): 195–212. https://doi.org/10.46787/pump.v8i.4862.

Full text

Abstract:

Panmagic permutations are permutations whose matrices are panmagic squares. Positions of 1-s in the latter describe maximal configurations of non-attacking queens on a toroidal chessboard. Some of them, affine panmagic permutations, can be conveniently described by linear formulas of modular arithmetic, and we show that their sets have remarkable algebraic properties when one multiplies three or more of them rather than just two. In group-theoretic terms, they are special cosets of the dihedral group in the group of all affine permutations. We also investigate decomposition of panmagic permuta

APA, Harvard, Vancouver, ISO, and other styles

46

Mykhalevych, Volodymyr, and Leonid Maidanevych. "USE OF THE MAPLE SYSTEM IN MATHEMATICAL PROBLEMS OF CRYPTOGRAPHY. PART 1. ELEMENTARY THEORY OF NUMBERS." Information technology and computer engineering 59, no. 1 (2024): 105–18. http://dx.doi.org/10.31649/1999-9941-2024-59-1-105-118.

Full text

Abstract:

On the basis of the analysis of literary sources, a conclusion was made about the relevance of using the environment of the Maple computer mathematics system for the purpose of creating software for conducting scientific research and creating educational and methodological materials for solving typical mathematical problems of cryptography. It is noted that the most famous and widespread cryptographic algorithm with a public key RSA is based on a number of problems of elementary number theory that can be solved using standard tools of the Maple system. This work examines the specified standard

APA, Harvard, Vancouver, ISO, and other styles

47

Tumanova, Elena Alexandrovna. "Computational Analysis of Quantitative Characteristics of some Residual Properties of Solvable Baumslag-Solitar Groups." Modeling and Analysis of Information Systems 28, no. 2 (2021): 136–45. http://dx.doi.org/10.18255/1818-1015-2021-2-136-145.

Full text

Abstract:

Let $G_{k}$ be defined as $G_{k} = \langle a, b;\ a^{-1}ba = b^{k} \rangle$, where $k \ne 0$. It is known that, if $p$ is some prime number, then $G_{k}$ is residually a finite $p$-group if and only if $p \mid k - 1$. It is also known that, if $p$ and $q$ are primes not dividing $k - 1$, $p < q$, and $\pi = \{p,\,q\}$, then $G_{k}$ is residually a finite $\pi$-group if and only if $(k, q) = 1$, $p \mid q - 1$, and the order of $k$ in the multiplicative group of the field $\mathbb{Z}_{q}$ is a $p$\-number. This paper examines the question of the number of two-element sets of prime numbers th

APA, Harvard, Vancouver, ISO, and other styles

48

Lattanzi, Daniele. "Computer Simulation Model of Prime Numbers." Journal of Advances in Mathematics and Computer Science 38, no. 8 (2023): 101–21. http://dx.doi.org/10.9734/jamcs/2023/v38i81794.

Full text

Abstract:

Prime numbers represent one of the major open problems in number theory mostly in that at present it is not possible to state that the induction principle holds for them. The methodology of experimental mathematics has been little endeavored in this field thus the present report deals with an innovative approach to the problem of primes treated as raw experimental data and as elements of larger and larger finite sequences {Pn}. The modified Chi-square function in the form -1/X2k(A,n/μ) with the ad-hoc A, k and μ parameters is the best-fit function of the finite sequences of primes {Pn}, like t

APA, Harvard, Vancouver, ISO, and other styles

49

LEWIS, ROBERT R. "Improved Upper Bounds for the Order of Some Classes of Abelian Cayley and Circulant Graphs of Diameter Two." Journal of Interconnection Networks 17, no. 03n04 (2017): 1741012. http://dx.doi.org/10.1142/s0219265917410122.

Full text

Abstract:

In the degree-diameter problem for Abelian Cayley and circulant graphs of diameter 2 and arbitrary degree d there is a wide gap between the best lower and upper bounds valid for all d, being quadratic functions with leading coefficient 1/4 and 1/2 respectively. Recent papers have presented constructions which increase the coefficient of the lower bound to be at or just below 3/8 for sparse sets of degree d related to primes of specific congruence classes. The constructions use the direct product of the multiplicative and additive subgroups of a Galois field and a specific cyclic group of copri

APA, Harvard, Vancouver, ISO, and other styles

50

Guo, Victor Zhenyu, Jinjiang Li, and Min Zhang. "Piatetski-Shapiro primes in arithmetic progressions." Ramanujan Journal, September 17, 2022. http://dx.doi.org/10.1007/s11139-022-00636-7.

Full text

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!