Results 61 to 70 of about 21,710,590 (82)
Stochastic orders of the sums of two exponential random variables
The sums of two exponential random variables are compared in the sense of likelihood ratio order. It is shown that, under some conditions, their likelihood ratio order does not exist and, if it exists, the complete comparison results can be determined ...
Chang, Kuo-Hwa
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A Note on Mean Value of Two-term Exponential Sums
Rev. Téc. Ing. Univ. Zulia., 2016 openaire +1 more source
On the mean value of the two-term exponential sums with Dirichlet characters [PDF]
Journal of Number Theory, 2007 The main purpose of this paper is using the analytic method to study the mean value properties of the two-term exponential sums with Dirichlet characters, and give an explicit formula for its fourth power ...
Tianping Zhang, Wenpeng Zhang
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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 }
Wen Peng Zhang
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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.
Wen Peng Zhang
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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.
Di Han
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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.
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On hybrid mean value of Dedekind sums and two-term exponential sums
Frontiers of Mathematics in China, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Wenpeng Zhang
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Upper bounds on a two-term exponential sum*
Science in China Series A: Mathematics, 2001The 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
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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 ...
Xingxing Lv
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