Monotonicity results for Dirichlet L-functions

被引：4

作者：

Dixit, Atul ^{[1
]}

Roy, Arindam ^{[2
]}

Zaharescu, Alexandru ^{[2
,3
]}

机构：

[1] Tulane Univ, Dept Math, New Orleans, LA 70118 USA

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Acad Romana, Simion Stoilow Inst Math, RO-014700 Bucharest, Romania

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2014年 / 410卷 / 01期

关键词：

Dirichlet L-function; Complete monotonicity; Logarithmically complete monotonicity; POLYGAMMA FUNCTIONS; HARMONIC MEASURE; GAMMA-FUNCTIONS; QUOTIENTS; ZEROS;

D O I：

10.1016/j.jmaa.2013.08.031

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present some monotonicity results for Dirichlet L-functions associated to real primitive characters. We show in particular that these Dirichlet L-functions are far from being logarithmically completely monotonic. Also, we show that, unlike in the case of the Riemann zeta function, the problem of comparing the signs of d(k)/ds(k) log L(s, chi) at any two points s(1), s(2) > 1 is subtler. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：307 / 315

页数：9

共 28 条

[1]

Alzer H, 2002, ANN ACAD SCI FENN-M, V27, P445

[2] Some classes of completely monotonic functions, II [J].