Inversion formula of Dirichlet polynomials and the approximate functional equation of Dirichlet's L-functions

被引：0

作者：

Wei Wang

机构：

[1] Department of Mathematics,

[2] Jinan 250 100,undefined

[3] P.R. China,undefined

[4] Current address: (c/o Prof. Dr. S.J. Patterson),undefined

[5] Mathematisches Institut,undefined

[6] Universität Göttingen,undefined

[7] Bunsenstr. 3-5,undefined

[8] D-37073 Göttingen,undefined

[9] Germany,undefined

来源：

Archiv der Mathematik | 1997年 / 69卷

关键词：

Error Term; Functional Equation; Inversion Formula; Critical Line; Dirichlet Polynomial;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

In this note, we prove an inversion formula for Dirichlet polynomials involving a non-principal character. By using Heath-Brown's upper-bound for Dirichlet's L-functions, we are able to obtain a non-trivial upper-bound for the error term in the q aspect. As an application we obtain an approximate functional equation for Dirichlet's L-functions to the right of the critical line with a sharp error term.

引用

页码：305 / 312

页数：7

共 50 条

[31] ON ZEROS OF DIRICHLET L-FUNCTIONS
CHEN, JG
SCIENTIA SINICA SERIES A-MATHEMATICAL PHYSICAL ASTRONOMICAL & TECHNICAL SCIENCES, 1986, 29 (09): : 897 - 913
[32] Nonvanishing of Dirichlet L-functions
Khan, Rizwanur
Ngo, Hieu T.
ALGEBRA & NUMBER THEORY, 2016, 10 (10) : 2081 - 2091
[33] ZEROS OF DIRICHLET L-FUNCTIONS
BALASUBRAMANIAN, R
MURTY, VK
ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE, 1992, 25 (05): : 567 - 615
[34] A functional relation for L-functions of graphs equivalent to the Riemann Hypothesis for Dirichlet L-functions
Friedli, Fabien
JOURNAL OF NUMBER THEORY, 2016, 169 : 342 - 352
[35] A new mean-value result for Dirichlet L-functions and polynomials
Harman, G
Watt, N
Wong, K
QUARTERLY JOURNAL OF MATHEMATICS, 2004, 55 : 307 - 324
[36] SIEGEL'S MASS FORMULA AND AVERAGES OF DIRICHLET L-FUNCTIONS OVER FUNCTION FIELDS
Maciak, Piotr
Morales, Jorge
ENSEIGNEMENT MATHEMATIQUE, 2011, 57 (3-4): : 393 - 422
[37] Wide moments of L-functions II: dirichlet L-functions
Nordentoft, Asbjorn Christian
QUARTERLY JOURNAL OF MATHEMATICS, 2023, 74 (01): : 365 - 387
[38] A note on Linnik’s approach to the Dirichlet L-functions
J. Kaczorowski
A. Perelli
Proceedings of the Steklov Institute of Mathematics, 2017, 296 : 115 - 124
[39] On the logarithmic derivatives of Dirichlet L-functions at s=1
Ihara, Yasutaka
Murty, V. Kumar
Shimura, Mahoro
ACTA ARITHMETICA, 2009, 137 (03) : 253 - 276
[40] On the Mean Square Value of Dirichlet’s L-functions
张文鹏
数学进展, 1990, (04) : 502 - 504

← 1 2 3 4 5 →