Results 11 to 20 of about 40 (38)
A New Sum Analogous to Gauss Sums and Its Fourth Power Mean
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 The main purpose of this paper is to use the analytic methods and the properties of Gauss sums to study the computational problem of one kind of new sum analogous to Gauss sums and give an interesting fourth power mean and a sharp upper bound estimate for it.
Shaofeng Ru +2 more
wiley +1 more source
New Mixed Exponential Sums and Their Application
Journal of Applied Mathematics, Volume 2014, Issue 1, 2014., 2014 The main purpose of this paper is to introduce a new mixed exponential sums and then use the analytic methods and the properties of Gauss sums to study the computational problems of the mean value involving these sums and give an interesting computational formula and a sharp upper bound estimate for these mixed exponential sums.
Yu Zhan, Xiaoxue Li, Ashraf Zenkour
wiley +1 more source
On the Generalization of Lehmer Problem and High‐Dimension Kloosterman Sums
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 For any fixed integer k ≥ 2 and integer r with (r, p) = 1, it is clear that there exist k integers 1 ≤ ai ≤ p − 1 (i = 1, 2, … , k) such that a1a2 ⋯ ak ≡ r mod p. Let N(k, r; p) denote the number of all (a1, a2, ⋯ ak) such that a1a2 ⋯ ak ≡ r mod p and 2†(a1 + a2 + ⋯ + ak).
Guohui Chen, Han Zhang, Kinkar Ch Das
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A Hybrid Mean Value Involving Dedekind Sums and the General Exponential Sums
The Scientific World Journal, Volume 2014, Issue 1, 2014., 2014 The main purpose of this paper is using the analytic method, A. Weil’s classical work for the upper bound estimate of the general exponential sums, and the properties of Gauss sums to study the hybrid mean value problem involving Dedekind sums and the general exponential sums and give a sharp asymptotic formula for it.
Jianghua Li, Tingting Wang, Reza Ansari
wiley +1 more source
On a Kind of Dirichlet Character Sums
Abstract and Applied Analysis, Volume 2013, Issue 1, 2013., 2013 Let p ≥ 3 be a prime and let χ denote the Dirichlet character modulo p. For any prime q with q < p, define the set Eq,p=a∣11≤a,a-≤p,aa-≡modp and a≡a-modq. In this paper, we study a kind of mean value of Dirichlet character sums ∑a≤p a∈Eq,p χ(a), and use the properties of the Dirichlet L‐functions and generalized Kloosterman sums to obtain an ...
Rong Ma +3 more
wiley +1 more source
Fourier expansions of complex‐valued Eisenstein series on finite upper half planes
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 We consider complex‐valued modular forms on finite upper half planes Hq and obtain Fourier expansions of Eisenstein series invariant under the groups Γ=SL(2,Fp) and GL(2,Fp). The expansions are analogous to those of Maass wave forms on the ordinary Poincaré upper half plane —the K‐Bessel functions being replaced by Kloosterman sums.
Anthony Shaheen, Audrey Terras
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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
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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
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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
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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