Results 11 to 20 of about 271 (57)
Note on the quadratic Gauss sums
International Journal of Mathematics and Mathematical Sciences, Volume 25, Issue 3, Page 167-173, 2001., 2001 Let p be an odd prime and {χ(m) = (m/p)}, m = 0, 1, …, p − 1 be a finite arithmetic sequence with elements the values of a Dirichlet character χ modp which are defined in terms of the Legendre symbol (m/p), (m, p) = 1. We study the relation between the Gauss and the quadratic Gauss sums.
George Danas
wiley +1 more source
The hybrid power mean of quartic Gauss sums and Kloosterman sums
Open Mathematics, 2017 The main purpose of this paper is using the analytic method and the properties of the classical Gauss sums to study the computational problem of one kind fourth hybrid power mean of the quartic Gauss sums and Kloosterman sums, and give an exact ...
Xiaoxue Li, Jiayuan Hu
doaj +1 more source
Open Mathematics, 2018 The main purpose of this paper is to study the computational problem of one kind hybrid power mean involving two-term exponential sums and quartic Gauss sums using the analytic method and the properties of the classical Gauss sums, and to prove some ...
Shen Shimeng
doaj +1 more source
IGUSA’S CONJECTURE FOR EXPONENTIAL SUMS: OPTIMAL ESTIMATES FOR NONRATIONAL SINGULARITIES
Forum of Mathematics, Pi, 2019 We prove an upper bound on the log canonical threshold of a hypersurface that satisfies a certain power condition and use it to prove several generalizations of Igusa’s conjecture on exponential sums, with the log canonical threshold in the exponent of ...
RAF CLUCKERS +2 more
doaj +1 more source
On the hybrid power mean of two kind different trigonometric sums
Open Mathematics, 2019 The main purpose of this paper is using the analytic method, the properties of trigonometric sums and Gauss sums to study the computational problem of one kind hybrid power mean involving two different trigonometric sums, and give an interesting ...
Zhuoyu Chen, Wenpeng Zhang
doaj +1 more source
, 2006 Let $p$ be a prime, and let $n>0$ and $r$ be integers. In this paper we study Fleck's quotient $$F_p(n,r)=(-p)^{-\lfloor(n-1)/(p-1)\rfloor} \sum_{k=r(mod p)}\binom {n}{k}(-1)^k\in Z.$$ We determine $F_p(n,r)$ mod $p$ completely by certain number ...
Sun, Zhi-Wei, Wan, Daqing
core +5 more sources
Short Kloosterman sums to powerful modulus
, 2016 We obtain the estimate of incomplete Kloosterman sum to powerful modulus $q$.
Korolev, Maxim A.
core +1 more source
The balanced Voronoi formulas for GL(n)
, 2017 In this paper we show how the GL(N) Voronoi summation formula of [MiSc2] can be rewritten to incorporate hyper-Kloosterman sums of various dimensions on both sides.
Miller, Stephen D., Zhou, Fan
core +1 more source
A note on the sign (unit root) ambiguities of Gauss sums in index 2 and 4 cases
, 2009 Recently, the explicit evaluation of Gauss sums in the index 2 and 4 cases have been given in several papers (see [2,3,7,8]). In the course of evaluation, the sigh (or unit root) ambiguities are unavoidably occurred.
B. C. Berndt +15 more
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On the generalized exponential sums and their fourth power mean
Open MathematicsThe main purpose of this article is to study the calculating problem of the fourth power mean of the two-term exponential sums and provide an accurate calculating formula for utilizing analytical methods and character sums’ properties. In the meantime, a
Liu Wencong, Ning Shushu
doaj +1 more source