Results 221 to 230 of about 134,188,628 (239)

On the Dedekind Sums and Two-Term Exponential Sums

Chinese Annals of Mathematics Series B, 2015
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Di Han
exaly   +2 more sources

Upper Bounds on a Two-Term Exponential Sum

Science in China Series A: Mathematics, 2001
The authors derive upper bounds for mixed exponential sums of type \[ S( \chi, a x^n + bx, p^m) = \sum_{_{\substack{ x=1\\ p \nmid x}}}^{p^m} \chi(x) e_{p^m}(a x^n + bx), \] where \(p^m\) is a prime power with \(m \geq 2\), \(a,b\) are integers, \(n \geq 2\), \(\chi\) is a multiplicative character mod \(p^m\) and \(e_{p^m}(x) = \exp(2 \pi i x/p^m ...
Todd Cochrane, Zhiyong Zheng
exaly   +3 more sources

On the Mean Value of the Two-Term Exponential Sums With Dirichlet Characters

Journal of Number Theory, 2007
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Tianping Zhang, Wenpeng Zhang, Zhefeng Xu   +2 more
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On Hybrid Mean Value of Dedekind Sums and Two-Term Exponential Sums

Frontiers of Mathematics in China, 2011
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Wenpeng Zhang
exaly   +3 more sources

A Hybrid Mean Value Involving Two-Term Exponential Sums and Polynomial Character Sums [PDF]

Czechoslovak Mathematical Journal, 2014
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exaly   +2 more sources

On the Hybrid Power Mean Involving the Two-Term Exponential Sums and Polynomial Character Sums

Chinese Annals of Mathematics, Series B, 2020
For any integer \(q \geq 3\), the high-dimensional Kloosterman sums \(K\left(c_{1}, c_{2}, \ldots, c_{k}, m ; q\right)\) are defined as follows: \[ K\left(c_{1}, c_{2}, \ldots, c_{k}, m ; q\right)=\mathop{\sum'}_{a_{1}=1}^{q} \cdots \mathop{\sum'}_{a_{k}=1}^{q} e\left(\frac{c_{1} a_{1}+\cdots+c_{k} a_{k}+m \bar{a}_{1} \cdots \bar{a}_{k}}{q}\right ...
Lv, Xingxing, Li, Xiaoxue
openaire   +1 more source

The mean value involving Dedekind sums and two-term exponential sums

Science China Mathematics, 2011
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Wang, Tingting, Pan, Xiaowei
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A new two-term exponential sums and its fourth power mean

Rendiconti del Circolo Matematico di Palermo Series 2, 2023
In the paper under review, the authors prove that for any odd prime \(p\), \[ C_4(p):=\sum_{m=0}^{p-1}\left|\sum_{n=0}^{p-1}\mathrm{e}\left(\frac{n^2(m+n)}{p}\right)\right|^4=2p^3+O(p^{5/2}), \] where \(\mathrm{e}(x)=e^{2\pi ix}\). They consider two cases when \(p-1\) is divisible by \(3\) or not.
Wang Xuexia, Wang Li
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On the Fourth Power Mean of Generalized Two-Term Exponential Sums [PDF]

Bulletin of the Korean Mathematical Society, 2013
In this paper, we use the elementary method and the theory of complex functions to study the computational problem of the fourth power mean of the generalized two-term exponential sums, and give two exact identities for them.
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The Hybrid Power Moment of Character Sums and Two-Term Exponential Sums

JP Journal of Algebra, Number Theory and Applications
This paper focuses on the investigation of the hybrid power mean concerning some special character sums of polynomials and the two-term exponential sums by utilizing analytical approaches and the nature of Gauss sums to give two sharp asymptotic formulae for them.
exaly   +3 more sources