Results 221 to 230 of about 22,813,091 (239)

On the Sixth Power Mean of the Two-Term Exponential Sums

Acta Mathematica Sinica, English Series, 2022
The article is devoted to the calculation problem of the sixth power mean of the two-term exponential sums. The main result is the following theorem. Let \(p>3\) be a prime and \(n\) be an integer. Then we have the identity \[ \sum_{m=1}^{p-1}\left|\sum_{a=0}^{p-1} e\left(\frac{m a^3+n a}{p}\right)\right|^6= \begin{cases}5 p^3 \cdot(p-1), & \text { if }
Wen Peng Zhang
exaly   +3 more sources

On the Character Sum of Polynomials and the Two-Term Exponential Sums

Acta Mathematica Sinica, English Series, 2020
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wen Peng Zhang
exaly   +3 more sources

On the Dedekind Sums and Two-Term Exponential Sums

Chinese Annals of Mathematics Series B, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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 Hybrid Mean Value of Dedekind Sums and Two-Term Exponential Sums

Frontiers of Mathematics in China, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenpeng Zhang
exaly   +3 more sources

On the Third Power Mean of Two-Term Exponential Sums

JP Journal of Algebra, Number Theory and Applications
Using the properties of character sums and the classical Gauss sums, we study the computational problem of one kind of third power mean of the two-term exponential sums, and give an exact computational formula.
Cui, Dewang, Wang, Li
exaly   +3 more sources

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

One Kind Sixth Power Mean of the Three-Term Exponential Sums

Open Mathematics, 2017
In this paper, we use the estimate for trigonometric sums and the properties of the congruence equations to study the computational problem of one kind sixth power mean of the three-term exponential sums.
Xiaoxue Li
exaly   +3 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
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Tingting, Pan, Xiaowei
openaire   +2 more sources