Murmurations of modular forms in the weight aspect

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

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

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
Journal	Algebra and Number Theory
Publication status	Accepted/In press - 11 Feb 2025

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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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year = "2025",

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language = "English",

journal = "Algebra and Number Theory",

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T1 - Murmurations of modular forms in the weight aspect

AU - Bober, Jonathan W

AU - Booker, Andrew R

AU - Lee, M

AU - Lowry-Duda, David

PY - 2025/2/11

Y1 - 2025/2/11

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.

M3 - Article (Academic Journal)

SN - 1937-0652

JO - Algebra and Number Theory

JF - Algebra and Number Theory

ER -

Murmurations of modular forms in the weight aspect

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