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Explicit Deuring–Heilbronn phenomenon for Dirichlet 𝐿-functions

Kübra Benli̇,Shivani Goel,Henry Twiss,Asif Zaman

2024 · DOI: 10.1090/proc/17450
Proceedings of the American Mathematical Society · 2 Citations

Abstract

Assuming the existence of a Landau–Siegel zero, we establish an explicit Deuring–Heilbronn zero repulsion phenomenon for Dirichlet L L -functions modulo q q . Our estimate is uniform in the entire critical strip, and improves over the previous best known explicit estimate  due to Thorner and Zaman [Forum Math. 36 (2024), pp. 1059–1080].