Tootfinder

On Murmurations and Trace Formulas
David Lowry-Duda
https://arxiv.org/abs/2506.01640 https://arxiv.org/pdf/2506.01640

On Murmurations and Trace Formulas
In recent work with Bober, Booker, Lee, Seymour-Howell, and Zubrilina, we proved murmuration behavior for Maass forms in the eigenvalue aspect and for modular forms in the weight aspect. Both used an approach based on the Selberg trace formula. But different trace formulas, including those due to Kuznetsov or Petersson, offer different variations. We examine murmurations from the perspective of different trace formulas and outline several families of $L$-functions where one can likely prove add…

Murmurations of Modular Forms and $p$-power Coefficients
Debanjana Kundu, Katharina Mueller
https://arxiv.org/abs/2507.00738 https://…

Murmurations of Modular Forms and $p$-power Coefficients
We extend the work of N. Zubrilina on murmuration of modular forms to the case when prime-indexed coefficients are replaced by squares of primes. Our key observation is that the shape of the murmuration density is the same.

Murmurations using Petersson trace formula
Chan Ieong Kuan, Didier Lesesvre
https://arxiv.org/abs/2507.11418 https://arxiv.org/pdf/25…

Murmurations using Petersson trace formula
We prove the murmuration phenomenon, which is a correlation between signs of functional equations and Fourier coefficients, in the case of modular forms in the weight aspect. We in particular improve the range of visibility of murmurations compared to previous results. This is the first approach to the murmuration phenomenon using a relative trace formula, showing its robustness.

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Poppy Ackroyd & Anna Lapwood:
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