MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms
Number Theory
2010-11-02 v1 Algebraic Geometry
Combinatorics
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.
Keywords
Cite
@article{arxiv.1010.5769,
title = {MacMahon's sum-of-divisors functions, Chebyshev polynomials, and Quasi-modular forms},
author = {George E. Andrews and Simon CF Rose},
journal= {arXiv preprint arXiv:1010.5769},
year = {2010}
}
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6 Pages