Murmurations of modular forms in the weight aspect

Jonathan W Bober; Andrew R Booker; M Lee; David Lowry-Duda

doi:10.2140/ant.2026.20.299

Murmurations of modular forms in the weight aspect

Jonathan W Bober, Andrew R Booker, M Lee, David Lowry-Duda^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

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Abstract

We prove the existence of “murmurations” in the family of holomorphic modular forms of level 1 and weight k → ∞, 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.

Original language	English
Pages (from-to)	299-332
Number of pages	34
Journal	Algebra and Number Theory
Volume	20
Issue number	2
DOIs	https://doi.org/10.2140/ant.2026.20.299
Publication status	Published - 16 Feb 2026

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© 2026 MSP (Mathematical Sciences Publishers).

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10.2140/ant.2026.20.299Licence: CC BY

https://doi.org/10.48550/arXiv.2310.07746

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title = "Murmurations of modular forms in the weight aspect",

abstract = "We prove the existence of “murmurations” in the family of holomorphic modular forms of level 1 and weight k → ∞, 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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AU - Lee, M

AU - Lowry-Duda, David

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N2 - We prove the existence of “murmurations” in the family of holomorphic modular forms of level 1 and weight k → ∞, 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.

AB - We prove the existence of “murmurations” in the family of holomorphic modular forms of level 1 and weight k → ∞, 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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DO - 10.2140/ant.2026.20.299

M3 - Article (Academic Journal)

SN - 1937-0652

VL - 20

SP - 299

EP - 332

JO - Algebra and Number Theory

JF - Algebra and Number Theory

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Murmurations of modular forms in the weight aspect

Abstract

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