On the Connection Between Riemann Hypothesis and a Special Class of Neural Networks
Machine Learning
2023-09-19 v1 Machine Learning
Abstract
The Riemann hypothesis (RH) is a long-standing open problem in mathematics. It conjectures that non-trivial zeros of the zeta function all have real part equal to 1/2. The extent of the consequences of RH is far-reaching and touches a wide spectrum of topics including the distribution of prime numbers, the growth of arithmetic functions, the growth of Euler totient, etc. In this note, we revisit and extend an old analytic criterion of the RH known as the Nyman-Beurling criterion which connects the RH to a minimization problem that involves a special class of neural networks. This note is intended for an audience unfamiliar with RH. A gentle introduction to RH is provided.
Keywords
Cite
@article{arxiv.2309.09171,
title = {On the Connection Between Riemann Hypothesis and a Special Class of Neural Networks},
author = {Soufiane Hayou},
journal= {arXiv preprint arXiv:2309.09171},
year = {2023}
}