Pacific Journal of Mathematics Vol. 111, No. 2, 1984

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A number theoretic series of I. Kasara

Harold George Diamond

Vol. 111 (1984), No. 2, 283–285

DOI: 10.2140/pjm.1984.111.283

Abstract

The series

S(x) = 1 + ∑ 1- ∑ --------1--------- k≥1 k! n n⋅⋅⋅n≤x logn1 logn2 ⋅⋅⋅lognk n11,n22,⋅⋅⋅k,nk>1

is interpreted as a statement about Beurling generalized prime numbers and is estimated by means of Beurling theory.

Mathematical Subject Classification 2000

Primary: 11N80

Milestones

Received: 8 September 1982

Published: 1 April 1984

Authors

Harold George Diamond
Department of Mathematics University of Illinois 1409 W Green Street Urbana IL 61801-2917 United States
http://www.math.uiuc.edu/~diamond