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Murmurations of Maass forms

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arxiv 2409.00765 v1 pith:2GQXODJB submitted 2024-09-01 math.NT

Andrew R. Booker , Min Lee , David Lowry-Duda , Andrei Seymour-Howell , Nina Zubrilina This is my paper · ORCID
classification math.NT
keywords formsmaassmurmurationsanalyticconductorcorrelationseigenvalueeigenvalues
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We prove the existence of murmurations in the family of Maass forms of weight 0 and level 1 with their Laplace eigenvalue parameter going to infinity (i.e., correlations between the parity and Hecke eigenvalues at primes growing in proportion to the analytic conductor).

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  1. Joint level-weight murmurations: prime averaging and the cubic pointwise range

    math.NT 2026-07 conditional novelty 8.0 of 10

    Unconditionally, joint averages of root-number-weighted prime traces of squarefree-level holomorphic newforms converge to an explicit atomic measure on rational squares for every K = X^ρ with 0 < ρ < 1.

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