On the Connection Between Riemann Hypothesis and a Special Class of
  Neural Networks
Soufiane Hayou
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.