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

DOI: 10.4236/apm.2024.146026, PP. 451-486

Keywords: Dirichlet L-Function, Absolute Tensor Product (Kurokawa Tensor Product), Euler Product

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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.

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