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math.NT2013
The q-Dixon sum Dirichlet series analogue
Geoffrey B Campbell
A few years ago, the concept of a D-analogue was introduced as a Dirichlet series analogue for the already known and well researched hypergeometric q-series. The D-analogue of the…
math.NT2012
Ramanujan and Eckford Cohen totients from Visible Point Identities
Geoffrey B. Campbell
We define an extension of the Ramanujan trigonometric function to arbitrary dimensions, and give the Dirichlet series generating function. The extension was first given by Eckford…
math.NT2012
Polylogarithm approaches to Riemann Zeta function zeroes
Geoffrey B Campbell
We use visible point vector identities to examine polylogarithms in the neighbourhood of the Riemann zeta function zeroes. New formulas limiting to the trivial zeroes and to the cr…