Identities for trigonometric divisor sums

Sun Kim

doi:10.1142/S1793042117500506

Identities for trigonometric divisor sums

Sun Kim^*

^*Corresponding author for this work

Department of Mathematics

University of Illinois at Urbana-Champaign

Research output: Contribution to journal › Journal article › peer-review

Abstract

The goal of this paper is to prove several identities for sums of the type (Equation Presented), where d(n) is the number of divisors of n and r₂(n) is the number of representations of n as a sum of two squares. Some of our identities involve weighted divisor functions, and most of our identities are new.

Original language	English
Pages (from-to)	957-975
Number of pages	19
Journal	International Journal of Number Theory
Volume	13
Issue number	4
DOIs	https://doi.org/10.1142/S1793042117500506
State	Published - 2017.05.1

Keywords

Bessel functions
circle problem
divisor problem
Ramanujan's lost notebook
Trigonometric sums
weighted divisor sums

Access to Document

10.1142/S1793042117500506

Cite this

@article{45d470aa44d641a29b44936dc92856d5,

title = "Identities for trigonometric divisor sums",

abstract = "The goal of this paper is to prove several identities for sums of the type (Equation Presented), where d(n) is the number of divisors of n and r2(n) is the number of representations of n as a sum of two squares. Some of our identities involve weighted divisor functions, and most of our identities are new.",

keywords = "Bessel functions, circle problem, divisor problem, Ramanujan's lost notebook, Trigonometric sums, weighted divisor sums",

author = "Sun Kim",

note = "Publisher Copyright: {\textcopyright} 2017 World Scientific Publishing Company.",

year = "2017",

month = may,

day = "1",

doi = "10.1142/S1793042117500506",

language = "English",

volume = "13",

pages = "957--975",

journal = "International Journal of Number Theory",

issn = "1793-0421",

number = "4",

}

TY - JOUR

T1 - Identities for trigonometric divisor sums

AU - Kim, Sun

PY - 2017/5/1

Y1 - 2017/5/1

N2 - The goal of this paper is to prove several identities for sums of the type (Equation Presented), where d(n) is the number of divisors of n and r2(n) is the number of representations of n as a sum of two squares. Some of our identities involve weighted divisor functions, and most of our identities are new.

AB - The goal of this paper is to prove several identities for sums of the type (Equation Presented), where d(n) is the number of divisors of n and r2(n) is the number of representations of n as a sum of two squares. Some of our identities involve weighted divisor functions, and most of our identities are new.

KW - Bessel functions

KW - circle problem

KW - divisor problem

KW - Ramanujan's lost notebook

KW - Trigonometric sums

KW - weighted divisor sums

UR - https://www.scopus.com/pages/publications/84994634520

U2 - 10.1142/S1793042117500506

DO - 10.1142/S1793042117500506

M3 - Journal article

AN - SCOPUS:84994634520

SN - 1793-0421

VL - 13

SP - 957

EP - 975

JO - International Journal of Number Theory

JF - International Journal of Number Theory

IS - 4

ER -

Identities for trigonometric divisor sums

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this