TITLE:
Euler Product Expressions of Absolute Tensor Products of Dirichlet L-Functions
AUTHORS:
Hidenori Tanaka, Shin-ya Koyama
KEYWORDS:
Dirichlet L-Function, Absolute Tensor Product (Kurokawa Tensor Product), Euler Product
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.14 No.6,
June
19,
2024
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.