%0 Journal Article
%T A Gamma Distribution Hypothesis for Prime $k$-tuples
%A J. LaChapelle
%J Mathematics
%D 2014
%I arXiv
%X We conjecture average counting functions for prime $k$-tuples based on a gamma distribution hypothesis for prime powers. The conjecture is closely related to the Hardy-Littlewood conjecture for $k$-tuples. Possessing average counting functions along with the exact functions allows to implicitly define pertinent $k$-tuple zeta functions. The $k$-tuple zeta functions in turn allow construction of $k$-tuple analogs of explicit formulae.
%U http://arxiv.org/abs/1406.6289v2