Monotonicity properties of L-functions

Sneha Chaubey, K. Paolina Koutsaki, Alexandru Zaharescu

Research output: Contribution to journalArticlepeer-review

Abstract

We present some monotonicity results for a class of Dirichlet series generalizing previously known results. The fact that ζ' (s) is in that class presents a first example of an arithmetic function for which the associated Dirichlet series is completely monotonic, but not logarithmically completely monotonic. Lastly, we use similar techniques to prove another formulation of the Riemann hypothesis for the L-function associated to the Ramanujan-tau function.

Original languageEnglish (US)
Pages (from-to)1238-1245
Number of pages8
JournalMathematische Nachrichten
Volume292
Issue number6
DOIs
StatePublished - Jun 2019

Keywords

  • 11M06
  • 11M26
  • 26A48
  • Ramanujan-tau L-function
  • complete monotonicity
  • first derivative of the Riemann zeta function
  • logarithmically complete monotonicity

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'Monotonicity properties of L-functions'. Together they form a unique fingerprint.

Cite this