On the Connection Between Riemann Hypothesis and a Special Class of Neural Networks
This work addresses a foundational mathematical problem for researchers in mathematics and theoretical machine learning, but it appears incremental as it revisits and extends an existing criterion.
The paper tackles the Riemann hypothesis by extending the Nyman-Beurling criterion to connect it to a minimization problem involving a special class of neural networks, but no concrete results or numbers are reported.
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.