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arXiv · 2509.21202

Asymptotics of partition parts in arithmetic progressions

Kathrin Bringmann·Caner Nazaroglu·Jan-Willem M. van Ittersum
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Abstract

We study the distribution of partition parts in arithmetic progressions and find asymptotic results that capture all exponentially growing terms. This is accomplished by studying the behavior of non-modular Eisenstein series that appear in their generating function and have expressions in terms of indefinite and false-indefinite theta functions.

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Kathrin Bringmann, Caner Nazaroglu, Jan-Willem M. van Ittersum. 2025-09-25. Asymptotics of partition parts in arithmetic progressions. https://arxiv.org/abs/2509.21202

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