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arXiv · 2310.07746

Murmurations of modular forms in the weight aspect

Jonathan Bober·Andrew R. Booker·Min Lee·David Lowry-Duda
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Abstract

We prove the existence of "murmurations" in the family of holomorphic modular forms of level $1$ and weight $k\to\infty$, that is, correlations between their root numbers and Hecke eigenvalues at primes growing in proportion to the analytic conductor. This is the first demonstration of murmurations in an archimedean family.

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Jonathan Bober, Andrew R. Booker, Min Lee, David Lowry-Duda. 2023-10-11. Murmurations of modular forms in the weight aspect. https://doi.org/10.2140/ant.2026.20.299

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