Identities for logarithmic means: A survey

Bruce C. Berndt; Sun Kim

doi:10.1007/978-1-4939-3201-6_1

Identities for logarithmic means: A survey

Bruce C. Berndt^*
, Sun Kim

^*Corresponding author for this work

Department of Mathematics

University of Illinois at Urbana-Champaign

Research output: Contribution to conference › Chapter › peer-review

1 Scopus citations

Abstract

We provide a survey of identities for sums of the type ∑_n≤x a(n) log(x=n): In each case, a(n) is an arithmetical function generated by a Dirichlet series satisfying a functional equation involving the gamma function. Moreover, all of the identities given in this paper feature infinite series of Bessel functions.

Original language	English
Title of host publication	Fields Institute Communications
Publisher	Springer New York LLC
Pages	1-10
Number of pages	10
DOIs	https://doi.org/10.1007/978-1-4939-3201-6_1
State	Published - 2015

Publication series

Name	Fields Institute Communications
Volume	77
ISSN (Print)	1069-5265

Access to Document

10.1007/978-1-4939-3201-6_1

Cite this

@inbook{4b74f30627a24bb882919fd7715acd25,

title = "Identities for logarithmic means: A survey",

abstract = "We provide a survey of identities for sums of the type ∑n≤x a(n) log(x=n): In each case, a(n) is an arithmetical function generated by a Dirichlet series satisfying a functional equation involving the gamma function. Moreover, all of the identities given in this paper feature infinite series of Bessel functions.",

author = "Berndt, \{Bruce C.\} and Sun Kim",

note = "Publisher Copyright: {\textcopyright} Springer Science+Business Media New York 2015.",

year = "2015",

doi = "10.1007/978-1-4939-3201-6\_1",

language = "English",

series = "Fields Institute Communications",

publisher = "Springer New York LLC",

pages = "1--10",

booktitle = "Fields Institute Communications",

}

TY - CHAP

T1 - Identities for logarithmic means

T2 - A survey

AU - Berndt, Bruce C.

AU - Kim, Sun

PY - 2015

Y1 - 2015

N2 - We provide a survey of identities for sums of the type ∑n≤x a(n) log(x=n): In each case, a(n) is an arithmetical function generated by a Dirichlet series satisfying a functional equation involving the gamma function. Moreover, all of the identities given in this paper feature infinite series of Bessel functions.

AB - We provide a survey of identities for sums of the type ∑n≤x a(n) log(x=n): In each case, a(n) is an arithmetical function generated by a Dirichlet series satisfying a functional equation involving the gamma function. Moreover, all of the identities given in this paper feature infinite series of Bessel functions.

UR - https://www.scopus.com/pages/publications/84946116009

U2 - 10.1007/978-1-4939-3201-6_1

DO - 10.1007/978-1-4939-3201-6_1

M3 - Chapter

AN - SCOPUS:84946116009

T3 - Fields Institute Communications

SP - 1

EP - 10

BT - Fields Institute Communications

PB - Springer New York LLC

ER -

Identities for logarithmic means: A survey

Abstract

Publication series

Access to Document

Other files and links

Fingerprint

Cite this