MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms

George E. Andrews, Simon C.F. Rose

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We investigate a relationship between MacMahon's generalized sum-of-divisors functions and Chebyshev polynomials of the first kind. This determines a recurrence relation to compute these functions, as well as proving a conjecture of MacMahon about their general form by relating them to quasi-modular forms. These functions arise as solutions to a curve-counting problem on Abelian surfaces.

Original languageEnglish (US)
Pages (from-to)97-103
Number of pages7
JournalJournal fur die Reine und Angewandte Mathematik
Volume2013
Issue number676
DOIs
StatePublished - Jan 1 2013

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Sum of divisors
Divisor Function
Modular Forms
Chebyshev Polynomials
Polynomials
Abelian Surfaces
Counting Problems
Recurrence relation
Curve

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

Cite this

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MacMahon's sum-of-divisors functions, Chebyshev polynomials, and quasi-modular forms. / Andrews, George E.; Rose, Simon C.F.

In: Journal fur die Reine und Angewandte Mathematik, Vol. 2013, No. 676, 01.01.2013, p. 97-103.

Research output: Contribution to journalArticle

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