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Monotonicity properties of L‐functions

Author

Listed:
  • Sneha Chaubey
  • K. Paolina Koutsaki
  • Alexandru Zaharescu

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.

Suggested Citation

  • Sneha Chaubey & K. Paolina Koutsaki & Alexandru Zaharescu, 2019. "Monotonicity properties of L‐functions," Mathematische Nachrichten, Wiley Blackwell, vol. 292(6), pages 1238-1245, June.
    • Handle: RePEc:bla:mathna:v:292:y:2019:i:6:p:1238-1245
    DOI: 10.1002/mana.201700485
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