Euler Product Expressions of Absolute Tensor Products of Dirichlet L-Functions  

作　　者：Hidenori Tanaka Shin-ya Koyama Hidenori Tanaka;Shin-ya Koyama(Department of Biomedical Engineering, Toyo University, Saitama, Japan;Department of Mechanical Engineering, Toyo University, Saitama, Japan)

机构地区：[1]Department of Biomedical Engineering, Toyo University, Saitama, Japan [2]Department of Mechanical Engineering, Toyo University, Saitama, Japan

出　　处：《Advances in Pure Mathematics》2024年第6期451-486,共36页理论数学进展（英文）

摘　　要：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.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.

关 键 词：Dirichlet L-Function Absolute Tensor Product (Kurokawa Tensor Product) Euler Product 

分 类 号：O17[理学—数学]