Hybrid mean value of 2k-th power inversion of L-functions and general quartic Gauss sums

被引：0

作者：

Singh, Shikha ^{[1
]}

Tanti, Jagmohan ^{[1
]}

机构：

[1] Cent Univ Jharkhand, Ctr Appl Math, Ranchi 835205, Bihar, India

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2019年 / 129卷 / 02期

关键词：

Dirichlet L-functions; Gauss sum; hybrid power mean; asymptotic formula; WEIGHT;

D O I：

10.1007/s12044-018-0460-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we find the 2k-th power mean of the inversion of L-functions with the weight of the general quartic Gauss sums. We establish the results with the help of Dirichlet characters and properties of classical Gauss sums. We also describe asymptotic behaviour for it.

引用

页数：12

共 10 条

[1]

Apostol T.M., 1976, INTRO ANAL NUMBER TH

[2]

Davenport H., 1967, MULTIPLICATIVE NUMBE

[3]

[刘红艳 Liu Hongyan], 2004, [系统科学与数学, Journal of Systems Science and Mathematical Sciences], V24, P289

[4] On the 2m-th power mean of Dirichlet L-functions with the weight of trigonometric sums [J].

Ma, Rong ;

Zhang, Junhuai ;

Zhang, Yulong .

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2009, 119 (04) :411-421

[5]

Yi Y, 2000, J SYSTEMS SCI MATH S, V20, P346

[6]

[易媛 Yi Yuan], 2002, [数学进展, Advances in Mathematics], V31, P517

[7]

Zhang W, 1993, CHINESE J CONT MATH, V14, P1

[8] On the mean square value of L-functions with the weight of quadratic Gauss sums [J].

Zhang, Wenpeng ;

Duan, Ran .

JOURNAL OF NUMBER THEORY, 2017, 179 :77-87

[9] Moments of generalized quadratic Gauss sums weighted by L-functions [J].

Zhang, WP .

JOURNAL OF NUMBER THEORY, 2002, 92 (02) :304-314

[10] A hybrid mean value of the inversion of L-functions and general quadratic gauss sums [J].

Zhang, WP ;

Deng, YP .

NAGOYA MATHEMATICAL JOURNAL, 2002, 167 :1-15

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