Explicit formulae for a class of Dirichlet series

Donald Michael Redmond

Vol. 102 (1982), No. 2, 413–435

DOI: 10.2140/pjm.1982.102.413

Abstract

In this paper we shall prove explicit formulae for Dirichlet series satisfying functional equations involving multiple gamma factors. We shall illustrate the general theorem by giving a generalization of the von Mangoldt formula and by proving the nonvanishing on the line of absolute convergence for a subclass of the Dirichlet series considered in the main theorem.

Mathematical Subject Classification

Primary: 10H10, 10H10

Milestones

Received: 22 October 1979

Revised: 1 September 1981

Published: 1 October 1982