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International Journal of Mathematics and Mathematical Sciences
Volume 16, Issue 2, Pages 359-372

Dirichlet summations and products over primes

21 Wurruk Avenue, Preston, Victoria 3072, Australia

Received 3 June 1991; Revised 1 July 1991

Copyright © 1993 Hindawi Publishing Corporation. 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.


We derive new classes of infinite products taken over the primes, for example expressing p(11pn)(1pm)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.