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2020 Explicit Zero-Free Regions and a $\tau$-Li-type Criterion
Neea Palojärvi
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Albanian J. Math. 14(1): 47-77 (2020). DOI: 10.51286/albjm/1608313766

Abstract

$\tau$-Li coefficients describe if a function satisfies the Generalized Riemann Hypothesis or not. In this paper we prove that certain values of the $\tau$-Li coefficients lead to existence or non-existence of certain zeros. The first main result gives explicit numbers $N_1$ and $N_2$ such that if all real parts of the $\tau$-Li coefficients are non-negative for all indices between $N_1$ and $N_2$, then the function has non zeros outside a certain region. According to the second result, if some of the real parts of the $\tau$-Li coefficients are negative for some index n between numbers $n_1$ and $n_2$, then there is at least one zero outside a certain region.

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Neea Palojärvi. "Explicit Zero-Free Regions and a $\tau$-Li-type Criterion." Albanian J. Math. 14 (1) 47 - 77, 2020. https://doi.org/10.51286/albjm/1608313766

Information

Published: 2020
First available in Project Euclid: 18 December 2020

zbMATH: 1441.11216
MathSciNet: MR4113635
Digital Object Identifier: 10.51286/albjm/1608313766

Subjects:
Primary: 11M26
Secondary: 11M06 , 11M41

Keywords: $\tau$-Li coefficients , explicit formulas , Li coefficients , zero-free regions

Rights: Copyright © 2020 Research Institute of Science and Technology (RISAT)

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Vol.14 • No. 1 • 2020
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