On murmurations

Timothy Nelson; Erick Ross; Maya Wassercug; Hui Xue

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arXiv · 2609.29631

On murmurations

Timothy Nelson·Erick Ross·Maya Wassercug·Hui Xue

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Abstract

In the recent paper ``Murmurations", Zubrilina showed that the Fourier coefficients of modular forms follow a certain murmuration pattern. The proof given in ``Murmurations" proceeded by estimating the terms of the Skoruppa-Zagier trace formula. However, a few technical issues arise in the proof, including an omission of certain Chebyshev factors that arise in summations from the Skoruppa-Zagier trace formula. In this work, we address these issues to solidify the proof.

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Timothy Nelson, Erick Ross, Maya Wassercug, Hui Xue. 2026-08-28. On murmurations. https://arxiv.org/abs/2609.29631

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