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The error term in the truncated Perron formula for the logarithm of an L-function

Part of: Algebraic number theory: local and $p$-adic fields Algebraic number theory: global fields Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  09 March 2023

Stephan Ramon Garcia ,
Jeffrey Lagarias Open the ORCID record for Jeffrey Lagarias [Opens in a new window]  and
Ethan Simpson Lee Open the ORCID record for Ethan Simpson Lee [Opens in a new window]
Stephan Ramon Garcia
Affiliation:
Department of Mathematics and Statistics, Pomona College, 610 North College Avenue, Claremont, CA 91711, USA e-mail: stephan.garcia@pomona.edu
Jeffrey Lagarias
Affiliation:
Department of Mathematics, University of Michigan, 530 Church Street, Ann Arbor, MI 48109, USA e-mail: lagarias@umich.edu
Ethan Simpson Lee*
Affiliation:
School of Mathematics, University of Bristol, Fry Building, Woodland Road, Bristol BS8 1UG, UK
*
e-mail: ethan.lee@bristol.ac.uk
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Abstract

We improve upon the traditional error term in the truncated Perron formula for the logarithm of an L-function. All our constants are explicit.

Keywords

Perron formulaL-functionzeta functionLambert function

MSC classification

Primary: 11M06: $zeta (s)$ and $L(s, chi)$ 11R42: Zeta functions and $L$-functions of number fields 11S40: Zeta functions and $L$-functions
Type
Article
Information
Canadian Mathematical Bulletin , Volume 66 , Issue 4 , December 2023 , pp. 1122 - 1134
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Copyright
© The Author(s), 2023. Published by Cambridge University Press on behalf of The Canadian Mathematical Society

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Footnotes

S.R.G. was supported by NSF Grant DMS-2054002.

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