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

Neea Palojärvi

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 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.

Sidor (från-till)47–77
TidskriftAlbanian Journal of Mathematics
StatusPublicerad - 2020
MoE-publikationstypA1 Tidskriftsartikel-refererad

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