Explicit zero-free regions and a τ-Li-type criterion

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Abstract

 τ-Li coefficients describe if a function satisfies the GeneralizedRiemann Hypothesis or not. In this paper we prove that certain values of theτ-Li coefficients lead to existence or non-existence of certain zeros. The firstmain result gives explicit numbers N1 and N2 such that if all real parts ofthe τ-Li coefficients are non-negative for all indices between N1 and N2, thenthe function has non zeros outside a certain region. According to the secondresult, if some of the real parts of the τ-Li coefficients are negative for someindex n between numbers n1 and n2, then there is at least one zero outside acertain region.

Original languageUndefined/Unknown
Pages (from-to)47–77
JournalAlbanian Journal of Mathematics
Volume14
Issue number1
Publication statusPublished - 2020
MoE publication typeA1 Journal article-refereed

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