Note on a note of Goldston and Suriajaya

TL;DR

This paper demonstrates that a weak form of the Hardy-Littlewood conjecture on Goldbach's problem can be used to disprove the existence of exceptional zeros of Dirichlet L-functions, strengthening previous results.

Contribution

It shows that assuming a weak Hardy-Littlewood conjecture suffices to eliminate exceptional zeros, advancing understanding of L-functions and prime distribution.

Findings

Weak Hardy-Littlewood conjecture implies no exceptional zeros of Dirichlet L-functions.

Strengthens previous results linking prime conjectures to L-function zeros.

Provides new conditional disproof of exceptional zeros based on prime distribution assumptions.

Abstract

We show that the assumption of a weak form of the Hardy-Littlewood conjecture on the Goldbach problem suffices to disprove the possible existence of exceptional zeros of Dirichlet L-functions. This strengthens a result of the authors named in the title.