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

^*Corresponding author for this work

Department of Mathematics

University of Illinois at Urbana-Champaign
Romanian Academy

Research output: Contribution to journal › 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
Article number	51
Journal	Ramanujan Journal
Volume	67
Issue number	3
DOIs	https://doi.org/10.1007/s11139-025-01104-8
State	Published - 2025.07

Keywords

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

Quacquarelli Symonds(QS) Subject Topics

Mathematics

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10.1007/s11139-025-01104-8

Cite this

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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 = "Publisher Copyright: {\textcopyright} The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.",

year = "2025",

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doi = "10.1007/s11139-025-01104-8",

language = "English",

volume = "67",

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T1 - Metric properties of Farey series and connections to the Riemann hypothesis

AU - Kim, Sun

AU - Zaharescu, Alexandru

N1 - Publisher Copyright: © The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2025.

PY - 2025/7

Y1 - 2025/7

N2 - 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.

AB - 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.

KW - Dirichlet L-functions

KW - Distances between sets

KW - Farey fractions

KW - Parity constraints

KW - Riemann zeta function

UR - https://www.scopus.com/pages/publications/105005779414

U2 - 10.1007/s11139-025-01104-8

DO - 10.1007/s11139-025-01104-8

M3 - Journal article

AN - SCOPUS:105005779414

SN - 1382-4090

VL - 67

JO - Ramanujan Journal

JF - Ramanujan Journal

IS - 3

M1 - 51

ER -

Metric properties of Farey series and connections to the Riemann hypothesis

Abstract

Keywords

Quacquarelli Symonds(QS) Subject Topics

Access to Document

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