Li coefficients as norms of functions in a model space

TL;DR

This paper links Li coefficients, crucial for the Riemann hypothesis, to norms of specific functions, providing a new perspective akin to Weil's criterion for understanding the hypothesis.

Contribution

It establishes that the Riemann hypothesis holds if and only if all Li coefficients are norms of particular functions, offering a novel functional-analytic criterion.

Findings

Li coefficients are equivalent to norms of functions in a model space.

Provides a new functional-analytic criterion for the Riemann hypothesis.

Connects Li coefficients to Weil's criterion for the first time.

Abstract

It is known that the nonnegativity of Li coefficients is a necessary and sufficient condition for the Riemann hypothesis. We show that it is a necessary and sufficient condition for the Riemann hypothesis that all Li coefficients are norms of certain concrete functions on the real line. Such conditional formulas for Li coefficients are understood as a kind of Weil's criterion for the Riemann hypothesis.