Integer factorization and finite Fourier series expansion

Given two integers a and k > 0, the number of factorizations of a (mod k ) is the number of ordered pairs ( s, t ) ∈ {0 , 1 , . . . , k − 1} 2 satisfying s · t ≡ a (mod k ). This number is known to be expressible by a formula involving the greatest common divisor function. Motivated by such a for...

Full description

Saved in:
Bibliographic Details
Published inLithuanian mathematical journal Vol. 61; no. 2; pp. 274 - 284
Main Authors Yangklan, Pussadee, Laohakosol, Vichian, Mavecha, Sukrawan
Format Journal Article
LanguageEnglish
Published New York Springer US 01.04.2021
Springer Nature B.V
Subjects
Actuarial Sciences
Fourier series
Mathematical functions
Mathematics
Mathematics and Statistics
Number Theory
Ordinary Differential Equations
Probability Theory and Stochastic Processes
Series expansion
convolution
finite Fourier series
factorization
unitary divisor
11A25
Online AccessGet full text

Cover

More Information
Summary:Given two integers a and k > 0, the number of factorizations of a (mod k ) is the number of ordered pairs ( s, t ) ∈ {0 , 1 , . . . , k − 1} 2 satisfying s · t ≡ a (mod k ). This number is known to be expressible by a formula involving the greatest common divisor function. Motivated by such a formula, we derive several formulae counting the number of factorizations of a (mod k ) subject to certain other natural restrictions. Some of these formulae are obtained as consequences of finite Fourier series expansions of the greatest common divisor function, whereas some are shown to be closely connected with the notion of unitary divisors.
Bibliography:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0363-1672
1573-8825
DOI:10.1007/s10986-020-09506-5