Siegel zeros under Goldbach conjectures

Abstract: A Landau-Siegel zero is a possible though unwelcome counter-example to the Generalised Riemann Hypothesis. Proving its absence unconditionally is clearly a difficult problem. We will discuss some results by assuming plausible conjectures on the Goldbach problem: the Hardy-Litllewood one (1923), a weak form due to Fei (2016), and a weaker form that we studied more recently (Bhowmik-Halupczok, in: Proceedings of CANT 2019 and 2020). Continuing on these lines, Friedlander-Goldston-Iwaniec-Suriajaya (2022) showed that the assumption of Fei's conjecture is enough to disprove the existence of Siegel zeros.

number theory

Audience: researchers in the discipline

Combinatorial and additive number theory (CANT 2022)