Critical zeros of lacunary L-functions

TL;DR

This paper demonstrates that, under certain assumptions, all zeros of the Riemann zeta function within specific segments lie on the critical line, extending to a broader class of lacunary L-functions.

Contribution

It proves that a hundred percent of zeros are on the critical line for certain segments of the Riemann zeta function, assuming the existence of exceptional discriminants.

Findings

All zeros in specific segments are on the critical line

Results apply to lacunary L-functions

Conditional on exceptional discriminants

Abstract

Assuming the existence of a sequence of exceptional discriminants of quadratic fields, we show that a hundred percent of zeros of the Riemann zeta function are on the critical line in specific segments. This is a special case of a more general statement for lacunary $L$-functions.