On the value-distribution of the difference between logarithms of two symmetric power $L$-functions

Kohji Matsumoto; Yumiko Umegaki

On the value-distribution of the difference between logarithms of two symmetric power $L$-functions

Number Theory 2016-03-25 v1

Authors: Kohji Matsumoto , Yumiko Umegaki

Abstract

We consider the value distribution of the difference between logarithms of two symmetric power $L$ -functions at $s=\sigma > 1/2$ . We prove that certain averages of those values can be written as integrals involving a density function which is constructed explicitly.

Keywords

value distribution symmetric power $L$-functions logarithm difference density function explicit construction analytic number theory mean value

Cite

@article{arxiv.1603.07436,
  title  = {On the value-distribution of the difference between logarithms of two symmetric power $L$-functions},
  author = {Kohji Matsumoto and Yumiko Umegaki},
  journal= {arXiv preprint arXiv:1603.07436},
  year   = {2016}
}

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36 pages

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