Metric properties of Farey series and connections to the Riemann hypothesis

Sun Kim; Alexandru Zaharescu

doi:10.1007/s11139-025-01104-8

Metric properties of Farey series and connections to the Riemann hypothesis

Sun Kim, Alexandru Zaharescu

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider distances between sets of Farey fractions defined by parity constraints and establish connections with upper bounds for the real parts of zeros of the Riemann zeta function and of the Dirichlet L-function associated to the non-principal Dirichlet character modulo 4.

Original language	English (US)
Article number	51
Journal	Ramanujan Journal
Volume	67
Issue number	3
Early online date	May 22 2025
DOIs	https://doi.org/10.1007/s11139-025-01104-8
State	Published - Jul 2025

Keywords

Dirichlet L-functions
Distances between sets
Farey fractions
Parity constraints
Riemann zeta function

ASJC Scopus subject areas

Algebra and Number Theory

Online availability

10.1007/s11139-025-01104-8

Library availability

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title = "Metric properties of Farey series and connections to the Riemann hypothesis",

abstract = "We consider distances between sets of Farey fractions defined by parity constraints and establish connections with upper bounds for the real parts of zeros of the Riemann zeta function and of the Dirichlet L-function associated to the non-principal Dirichlet character modulo 4.",

keywords = "Dirichlet L-functions, Distances between sets, Farey fractions, Parity constraints, Riemann zeta function",

author = "Sun Kim and Alexandru Zaharescu",

note = "The first author\u2019s research was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. RS-2023-00240168).",

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AU - Kim, Sun

AU - Zaharescu, Alexandru

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KW - Dirichlet L-functions

KW - Distances between sets

KW - Farey fractions

KW - Parity constraints

KW - Riemann zeta function

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Metric properties of Farey series and connections to the Riemann hypothesis

Abstract

Keywords

ASJC Scopus subject areas

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