Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers

2025/06/05 by Matsusaka, Toshiki, Suzuki, Miyu
#11F27 #17B10 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2506.04722

Abstract

We extend the recently developed theory of Roehrig and Zwegers on indefinite theta functions to prove certain power series are modular forms. As a consequence, we obtain several power series identities for powers of the generating function of triangular numbers. We also show that these identities arise as specializations of denominator identities of affine Lie superalgebras.

Citations

• Theta Series for Quadratic Forms of Signature (n-1,1) with (Spherical)\n Polynomials
• Denominator identity for affine Lie superalgebras with zero dual Coxeter number
• Weyl denominator identity for affine Lie superalgebras with non-zero dual Coxeter number
• Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions
• Integrable highest weight modules over affine superalgebras and number theory

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