Riemann, Thorin, van Dantzig Pairs, Wald Couples and Hadamard Factorisation
Probability
2026-05-01 v8
Abstract
Zeros of entire functions can be found using either the Fourier methods of Riemann-Polya or the Generalized Gamma Convolution (GGC) methods of Thorin-Bondesson. This connection is based on a duality between the Hadamard-Weierstrass factorisation and van Dantzig Pairs-Wald couples of random variables. We demonstrate the methodology on particular functions including the Riemann zeta and xi-functions, Ramanujan's tau function, L-functions and Gamma and Hyperbolic functions.
Cite
@article{arxiv.1804.10043,
title = {Riemann, Thorin, van Dantzig Pairs, Wald Couples and Hadamard Factorisation},
author = {Nicholas G. Polson},
journal= {arXiv preprint arXiv:1804.10043},
year = {2026}
}