The Euler Product expressions of the absolute tensor products of the Dirichlet $L$-functions

Hidenori Tanaka

The Euler Product expressions of the absolute tensor products of the Dirichlet $L$-functions

Number Theory 2020-09-14 v2

Authors: Hidenori Tanaka

Abstract

In this paper, we calculate the absolute tensor square of the Dirichlet $L$ -functions and show that it is expressed as an Euler product over pairs of primes. The method is to construct an equation to link primes to a series which has the factors of the absolute tensor product of the Dirichlet $L$ -functions. This study is a generalization of Akatsuka's theorem on the Riemann zeta function, and gives a proof of Kurokawa's prediction proposed in 1992.

Keywords

dirichlet l-functions absolute tensor product euler product riemann zeta function prime pairs

Cite

@article{arxiv.2008.07752,
  title  = {The Euler Product expressions of the absolute tensor products of the Dirichlet $L$-functions},
  author = {Hidenori Tanaka},
  journal= {arXiv preprint arXiv:2008.07752},
  year   = {2020}
}

Comments

35 pages

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