Monotonicity Results for Dirichlet L-functions

2013/04/03 by Atul Dixit, Dixit, Atul, Arindam Roy +3
Mathematics · #11M06 #11M26 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11M06 #msc:11M26

paper · pdf · doi:10.48550/arxiv.1304.0827

13 pages, 2 figures, submitted for publication

arxiv created 2013/04/09 · arxiv updated 2013/04/10

Abstract

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,χ) at any two points s₁, s₂>1 is more subtle.

Related

• Investigation about a statement equivalent to Riemann Hypothesis (RH) applied to Dirichlet primitive L functions
• A note on entire L-functions
• Non-vanishing of Dirichlet L-functions at the Central Point
• Asymptotic formulas for the logarithm of general L-functions at and near s=1
• A one-formula proof of the nonvanishing of L-functions of real characters at 1