Elementary methods in the study of Deuring-Heilbronn Phenomenon
Chiara Bellotti, Giuseppe Puglisi
TL;DR
This paper improves elementary estimates on how zeros of the Riemann zeta function and L-functions influence exceptional zeros, enhancing understanding of the Deuring-Heilbronn Phenomenon.
Contribution
It provides refined elementary bounds on the impact of zeros of zeta and L-functions on exceptional zeros, advancing previous results.
Findings
Better estimates for influence of zeta zeros on exceptional zeros
Improved bounds for zeros of L-functions in non-principal characters
Enhanced understanding of Deuring-Heilbronn Phenomenon
Abstract
The aim of this work is to improve some elementary results regarding both the Deuring-Phenomenon and the Heilbronn-Phenomenon. We will give better estimates regarding both the influence of zeros of the Riemann zeta function on the exceptional zeros and that of the non-trivial zeros of arbitrary L-functions belonging to non-principal characters on the exceptional zeros.
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Taxonomy
TopicsMeromorphic and Entire Functions · Analytic Number Theory Research · Algebraic and Geometric Analysis