On a factorization of Riemann’s ζ function with respect to a quadratic field and its computation
نویسنده
چکیده
Let K be a quadratic field, and let ζK its Dedekind zeta function. In this paper we introduce a factorization of ζK into two functions, L1 and L2, defined as partial Euler products of ζK , which lead to a factorization of Riemann’s ζ function into two functions, p1 and p2. We prove that these functions satisfy a functional equation which has a unique solution, and we give series of very fast convergence to them. Moreover, when ∆K > 0 the general term of these series at even positive integers is calculated explicitly in terms of generalized Bernoulli numbers.
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