International Journal of Mathematics and Mathematical Sciences
Volume 16 (1993), Issue 2, Pages 359-372
doi:10.1155/S0161171293000444
Dirichlet summations and products over primes
21 Wurruk Avenue, Preston, Victoria 3072, Australia
Received 3 June 1991; Revised 1 July 1991
Copyright © 1993 Geoffrey B. Campbell. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We derive new classes of infinite products taken over the primes, for example
expressing
∏p(11−p−n)(1−p−m)−1
as an infinite produce of Riemann zeta functions, this product being taken over the set of rational
numbers α/β geater than zero with a relatively prime to βζ(n)∏α,βζ(αm+βn)1/β.