Identities involving the coefficients of a class of Dirichlet series. IV

Bruce C. Berndt

Type: Article

Publication Date: 1970-01-01

Citations: 71

DOI: https://doi.org/10.1090/s0002-9947-1970-0260685-5

Abstract

We consider a class of Dirichlet series satisfying a functional equation with gamma factors. We define a generalized Dirichlet series that is analogous to the generalized zeta-function of Riemann. An analytic continuation for these generalized series is derived, and a few simple properties are established. Secondly, we prove a theorem on the Abel summation of Dirichlet series that satisfy Hecke’s functional equation.

Locations

Transactions of the American Mathematical Society - View - PDF

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