Journal of the Ramanujan Mathematical Society

Yasufumi Hashimoto ¹

Affiliations
1 Graduate School of Mathematics, Kyushu University, 6-10-1, Hakozaki, Fukuoka 812-8581, JP

Abstract

It is well-known that the Euler constant γ is considered as the constant term of the Laurent expansion at s=1 of the Riemann zeta function ζ(s). In this paper, we define the Euler constant γ_p as the constant term of the Laurent expansion of the zeta function ζ_p(s) given by the Euler product over elements of a prime set P, and establish the expression of γ_p as the sum over elements of P, which is similar to the one obtained by de la Vallee-Poussin [9].

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