Factorization theorems for relatively prime divisor sums, GCD sums and generalized Ramanujan sums

DOI10.1007/s11139-020-00323-5zbMath1472.11038arXiv1810.08373OpenAlexW3094300639MaRDI QIDQ829691

Hamed Mousavi, Maxie D. Schmidt

Publication date: 6 May 2021

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1810.08373

zbMATH Keywords

partition functionMöbius inversionmatrix factorizationtotient functiondivisor sum

Mathematics Subject Classification ID

Combinatorial aspects of partitions of integers (05A17) Arithmetic functions; related numbers; inversion formulas (11A25) Other results on the distribution of values or the characterization of arithmetic functions (11N64)

Uses Software

• DLMF
• OEIS

Cites Work

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• The Lambert series factorization theorem
• Factorization theorems for generalized Lambert series and applications
• On sums of averages of generalized Ramanujan sums
• Arithmetical properties of generalized Ramanujan sums
• On the Fourier transform of the greatest common divisor
• Menon's identity and arithmetical sums representing functions of several variables
• Generating Special Arithmetic Functions by Lambert Series Factorizations