Results 211 to 220 of about 167,996 (242)

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 }
Zhang, Wen Peng, Meng, Yuan Yuan
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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
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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 Dedekind sums and two-term exponential sums

Chinese Annals of Mathematics, Series B, 2015
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Han, Di, Wang, Tingting
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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.
Xuan Wang
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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
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ON TWO-TERM EXPONENTIAL SUMS AND A NEW FIFTH POWER MEAN

JP Journal of Algebra, Number Theory and Applications
The primary aim of this paper is to study the problem of a new fifth power mean of the two-term exponential sums. By employing elementary methods, the number of solutions to a few congruence equations is obtained. Besides certain properties of classical Gauss sums have been derived.
Yating Du
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On the hybrid mean value of two-term exponential sums and character sums of polynomials

Lithuanian Mathematical Journal
For \(q,m,n,u,v\) positive integers with \(q\geq 3\) and \(u>v\), the two term exponential sums of \(u\) degree is defined by \[ C(m, n, u, v; q) := \sum_{\substack{a=1 \\ (a,q)=1}}^{q} e\left(\frac{ma^u + na^v}{q}\right). \] With \(M,N\) positive integers, \(\chi\) any Dirichlet character modulo \(q\), and \(f\) a polynomial (over \(\mathbb{Z}\)), the
Sun, Zhangrui, Han, Di
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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.
Wang, Tingting, Zhang, Wenpeng
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A note on fourth power mean of the general two-term exponential sums

Mathematical Reports
Let $q$, $m$, $n$ be any integer with $q\ge 3$, and $\lambda$ a Dirichlet character $\bmod $ $q$. An explicit formula for the fourth power mean $$ \mathop{\sum}_{{m=1}\atop{(m,q)=1}}^{q} \biggl| \mathop{\sum}_{a=1}^{q} \lambda(a) e\biggl( \frac{ma^3+na}{q} \biggr) \biggr|^4 $$ is derived.
Mu, Yaya, Zhang, Tianping
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