Results 21 to 30 of about 211 (54)
Differences between powers of a primitive root
International Journal of Mathematics and Mathematical Sciences, Volume 29, Issue 6, Page 325-331, 2002., 2002 We study the set of differences {gx − gy(modp) : 1 ≤ x, y ≤ N} where p is a large prime number, g is a primitive root (modp), and p2/3 < N < p.
Marian Vâjâitu, Alexandru Zaharescu
wiley +1 more source
An asymptotic local–global theorem on heights of some Kleinian group orbits
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We prove an asymptotic local–global theorem on the heights of point orbits of thin subgroups of Bianchi groups in H3$\mathbb {H}^3$.
Xuanxuan Xiao, Xin Zhang
wiley +1 more source
Maass-Jacobi Poincar\'e series and Mathieu Moonshine [PDF]
, 2015 Mathieu moonshine attaches a weak Jacobi form of weight zero and index one to each conjugacy class of the largest sporadic simple group of Mathieu. We introduce a modification of this assignment, whereby weak Jacobi forms are replaced by semi-holomorphic
Bringmann, Kathrin +2 more
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Character sum, reciprocity, and Voronoi formula
Bulletin of the London Mathematical Society, Volume 57, Issue 12, Page 3797-3823, December 2025.Abstract We prove a novel four‐variable character sum identity that serves as a twisted, non‐Archimedean analog of Weber's integrals for Bessel functions. Using this identity and ideas from Venkatesh's thesis, we provide a short spectral proof of the Voronoi formulae for classical modular forms with character twists.
Chung‐Hang Kwan, Wing Hong Leung
wiley +1 more source
Some New Identities Related to Dedekind Sums Modulo a Prime
Journal of Mathematics, Volume 2024, Issue 1, 2024.The main purpose of this article is to use some identities of the classical Gauss sums, the properties of character sums, and Dedekind sums (modulo an odd prime) to study the computational problem of one‐kind mean values related to Dedekind sums and give some interesting identities for them.
Jiayuan Hu, Xiaogang Liu
wiley +1 more source
Journal of Mathematics, Volume 2024, Issue 1, 2024.The primary contribution of this paper is to research one kind special Kloosterman sums using analytic method. We translate one kind fourth power mean of the Kloosterman sums into the character sums of one kind polynomials. It is possible to construct an exact formula for the fourth power mean of one kind Kloosterman sums by computing the character ...
Shushu Ning, Xuexia Wang, Ming-Sheng Liu
wiley +1 more source
Ramanujan sums as supercharacters [PDF]
, 2012 The theory of supercharacters, recently developed by Diaconis-Isaacs and Andre, can be used to derive the fundamental algebraic properties of Ramanujan sums. This machinery frequently yields one-line proofs of difficult identities and provides many novel
Fowler, Christopher F. +2 more
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An Invitation to Additive Prime Number Theory [PDF]
, 2005 2000 Mathematics Subject Classification: 11D75, 11D85, 11L20, 11N05, 11N35, 11N36, 11P05, 11P32, 11P55.The main purpose of this survey is to introduce the inexperienced reader to additive prime number theory and some related branches of analytic number ...
Kumchev, A., Tolev, D.
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Bilinear forms with trace functions over arbitrary sets, and applications to Sato-Tate
, 2023 We prove non-trivial upper bounds for general bilinear forms with trace functions of bountiful sheaves, where the supports of two variables can be arbitrary subsets in $\mathbf{F}_p$ of suitable sizes.
Xi, Ping
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On some reasons for doubting the Riemann hypothesis [PDF]
, 2003 Several arguments against the truth of the Riemann hypothesis are extensively discussed. These include the Lehmer phenomenon, the Davenport-Heilbronn zeta-function, large and mean values of $|\zeta(1/2+it)|$ on the critical line, and zeros of a class of ...
Ivić, Aleksandar
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