On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions

Su Hu; Daeyeoul Kim; Min Soo Kim

doi:10.1016/j.jnt.2015.10.022

On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions

Su Hu
, Daeyeoul Kim
, Min Soo Kim^*

^*Corresponding author for this work

Department of Mathematics

South China University of Technology
National Institute for Mathematical Sciences
Kyungnam University

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

10 Scopus citations

Abstract

The Apostol-Dedekind sum with quasi-periodic Euler functions is an analogue of Apostol's definition of the generalized Dedekind sum with periodic Bernoulli functions. In this paper, using the Boole summation formula, we shall obtain the reciprocity formula for this sum.

Original language	English
Pages (from-to)	54-67
Number of pages	14
Journal	Journal of Number Theory
Volume	162
DOIs	https://doi.org/10.1016/j.jnt.2015.10.022
State	Published - 2016.05.1

Keywords

Boole summation formula
Dedekind sum
Euler polynomial
Quasi-periodic Euler functions

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10.1016/j.jnt.2015.10.022

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title = "On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions",

abstract = "The Apostol-Dedekind sum with quasi-periodic Euler functions is an analogue of Apostol's definition of the generalized Dedekind sum with periodic Bernoulli functions. In this paper, using the Boole summation formula, we shall obtain the reciprocity formula for this sum.",

keywords = "Boole summation formula, Dedekind sum, Euler polynomial, Quasi-periodic Euler functions",

author = "Su Hu and Daeyeoul Kim and Kim, \{Min Soo\}",

note = "Publisher Copyright: {\textcopyright} 2015 Elsevier Inc.",

year = "2016",

month = may,

day = "1",

doi = "10.1016/j.jnt.2015.10.022",

language = "English",

volume = "162",

pages = "54--67",

journal = "Journal of Number Theory",

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TY - JOUR

T1 - On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions

AU - Hu, Su

AU - Kim, Daeyeoul

AU - Kim, Min Soo

PY - 2016/5/1

Y1 - 2016/5/1

N2 - The Apostol-Dedekind sum with quasi-periodic Euler functions is an analogue of Apostol's definition of the generalized Dedekind sum with periodic Bernoulli functions. In this paper, using the Boole summation formula, we shall obtain the reciprocity formula for this sum.

AB - The Apostol-Dedekind sum with quasi-periodic Euler functions is an analogue of Apostol's definition of the generalized Dedekind sum with periodic Bernoulli functions. In this paper, using the Boole summation formula, we shall obtain the reciprocity formula for this sum.

KW - Boole summation formula

KW - Dedekind sum

KW - Euler polynomial

KW - Quasi-periodic Euler functions

UR - https://www.scopus.com/pages/publications/84949634203

U2 - 10.1016/j.jnt.2015.10.022

DO - 10.1016/j.jnt.2015.10.022

M3 - Journal article

AN - SCOPUS:84949634203

SN - 0022-314X

VL - 162

SP - 54

EP - 67

JO - Journal of Number Theory

JF - Journal of Number Theory

ER -

On reciprocity formula of Apostol-Dedekind sum with quasi-periodic Euler functions

Abstract

Keywords

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