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arXiv · 2506.04722

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

Toshiki Matsusaka·Miyu Suzuki
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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.

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Toshiki Matsusaka, Miyu Suzuki. 2025-06-05. Indefinite theta functions arising from affine Lie superalgebras and sums of triangular numbers. https://arxiv.org/abs/2506.04722

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