Vol. 103, No. 2, 1982

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An arithmetic Poisson formula

Bruce C. Berndt

Vol. 103 (1982), No. 2, 295–299
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 Σn=−∞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
Authors
Bruce C. Berndt
Mathematics
University of Illinois at Urbana-Champaign
1409 West Green St.
Urbana IL 61801
United States
http://www.math.uiuc.edu/~berndt/