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math.NT2012
A Finite Reflection Formula For A Polynomial Approximation To The Riemann Zeta Function
Stephen Crowley
The Riemann zeta function can be written as the Mellin transform of the unit interval map w(x) = floor(1/x)*(-1+x*floor(1/x)+x) multiplied by s((s+1)/(s-1)). A finite-sum approxima…
math.NT2012
Integral Transforms of the Harmonic Sawtooth Map, The Riemann Zeta Function, Fractal Strings, and a Finite Reflection Formula
Stephen Crowley
The harmonic sawtooth map w(x) of the unit interval onto itself is defined where it is shown that its fixed points are enumerated by generating functions involving the golden ratio…
math.NT2012★ 3 cited
Two New Zeta Constants: Fractal String, Continued Fraction, and Hypergeometric Aspects of the Riemann Zeta Function
Stephen Crowley
The Riemann zeta function at integer arguments can be written as an infinite sum of certain hypergeometric functions and more generally the same can be done with polylogarithms, fo…