3 citations · 3 across the 6 of their papers we have counts for
6 papers
A Sequence of Cauchy Sequences Which Is Conjectured to Converge to the Imaginary Parts of the Zeros of the Riemann Zeta Function
Stephen Crowley
The convergence of a sequence of Cauchy sequences is conjectured; which if shown to be true, would prove the Riemann hypothesis by way of LeClair and França's transcendental equati…
An Expression For The Argument of at Zeros on the Critical Line
Stephen Crowley
The function $S_n (t) = π\left( \frac{3}{2} - {frac} \left( \frac{\vartheta(t)}π \right) + \left( \lfloor \frac{t \ln \left( \frac{t}{2 πe}\right)}{2 π} + \frac{7}{8} \rfloor - n \…
The Laplacian of The Integral Of The Logarithmic Derivative of the Riemann-Siegel-Hardy Z-function
Stephen Crowley
The integral of the logarithmic derivative of the Hardy Z function , where $\vartheta (t…
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…
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…
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…