Results 201 to 210 of about 138,517 (219)

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

Acta Mathematica Sinica, English Series, 2020
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Wen Peng Zhang
exaly   +3 more sources

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

ON MIXED TWO-TERM EXPONENTIAL SUMS [PDF]

Journal of the Korean Mathematical Society, 2010
In this paper, we shall use analytic methods to study the hybrid mean value involving the mixed two-term exponential sums C(m, n, r, chi; q), and give several sharp asymptotic formulae.
exaly   +2 more sources

On the mean value of the two-term exponential sums with Dirichlet characters

Journal of Number Theory, 2007
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Zhefeng Xu, Tianping Zhang, Wenpeng Zhang   +2 more
exaly   +2 more sources

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

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 ...
Cochrane, Todd, Zheng, Zhiyong
openaire   +2 more sources

A hybrid mean value involving two-term exponential sums and polynomial character sums [PDF]

Czechoslovak Mathematical Journal, 2014
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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 ...
Xingxing Lv
exaly   +2 more sources

New identities involving certain Hardy sums and two-term exponential sums

Indian Journal of Pure and Applied Mathematics, 2022
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exaly   +3 more sources

A new two-term exponential sums and its fourth power mean

Rendiconti Del Circolo Matematico Di Palermo, 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.
Li Wang
exaly   +3 more sources