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On the Sixth Power Mean of the Two-term Exponential Sums
Acta Mathematica Sinica, English Series, 2022The 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 Character Sum of Polynomials and the Two-term Exponential Sums
Acta Mathematica Sinica, English Series, 2020zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lv, Xing Xing, Zhang, Wen Peng
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On the Dedekind sums and two-term exponential sums
Chinese Annals of Mathematics, Series B, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Han, Di, Wang, Tingting
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The mean value involving Dedekind sums and two-term exponential sums
Science China Mathematics, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wang, Tingting, Pan, Xiaowei
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On the hybrid mean value of two-term exponential sums and character sums of polynomials
Lithuanian Mathematical JournalFor \(q,m,n,u,v\) 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 the Hybrid Power Mean Involving the Two-Term Exponential Sums and Polynomial Character Sums
Chinese Annals of Mathematics, Series B, 2020For 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 THE THIRD POWER MEAN OF TWO-TERM EXPONENTIAL SUMS
JP Journal of Algebra, Number Theory and ApplicationsUsing 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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THE HYBRID POWER MOMENT OF CHARACTER SUMS AND TWO-TERM EXPONENTIAL SUMS
JP Journal of Algebra, Number Theory and ApplicationsThis 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.
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A note on fourth power mean of the general two-term exponential sums
Mathematical ReportsLet $q$, $m$, $n$ 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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