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

By George E. Andrews, S. Rose. 2010

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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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7f3ac0a4b45d8aee8558498db2d36e8038d031d2