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arXiv · 1804.10043

Riemann, Thorin, van Dantzig Pairs, Wald Couples and Hadamard Factorisation

Nicholas G. Polson
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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.

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Nicholas G. Polson. 2018-04-19. Riemann, Thorin, van Dantzig Pairs, Wald Couples and Hadamard Factorisation. https://arxiv.org/abs/1804.10043

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