Monotonicity results for Dirichlet L-functions

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:410

Article

Dixit, Atul¹  Roy, Arindam²  Zaharescu, Alexandru^2,3 

[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

关键词: Dirichlet L-function;    Complete monotonicity;    Logarithmically complete monotonicity;   

DOI  :  10.1016/j.jmaa.2013.08.031

来源: Elsevier

【 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.

【 授权许可】

Free