An arithmetic Poisson formula

Bruce C. Berndt

Vol. 103 (1982), No. 2, 295–299

DOI: 10.2140/pjm.1982.103.295

Abstract

Let a(n) denote any arithmetic function. Since most arithmetic functions that are encountered are defined on only the nonnegative integers, we define a(−n) = a(n) for each positive integer n. Our objective is to develop a Poisson type formula for Σ_n=−∞^∞a(n)f(n), where f belongs to a suitable class of functions. We conclude the paper with several applications of our arithmetic Poisson formula.

Mathematical Subject Classification

Primary: 10H25, 10H25

Secondary: 10G99, 10A20

Milestones

Received: 13 July 1978

Published: 1 December 1982