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Exceptional zeros, sieve parity, Goldbach

John B. Friedlander and Henryk Iwaniec

Vol. 1 (2022), No. 1, 13–39
Abstract

We survey connections between the possible existence of exceptional real zeros of Dirichlet L-functions and the sieve parity barrier and then show how recent work tying them to the Goldbach problem can be viewed in a considerably generalized framework.

Keywords
primes, sieves, exceptional zeros, Goldbach conjecture
Mathematical Subject Classification
Primary: 11M20, 11N05, 11N35, 11P32
Milestones
Received: 24 August 2021
Revised: 22 December 2021
Accepted: 15 January 2022
Published: 26 October 2022
Authors
John B. Friedlander
Department of Mathematics
University of Toronto
Toronto, ON
Canada
Henryk Iwaniec
Department of Mathematics
Rutgers University
Piscataway, NJ
United States