10 papers · 1 filter
Murmurations of modular forms in the weight aspect
Jonathan Bober, Andrew R. Booker, Min Lee +1
We prove the existence of "murmurations" in the family of holomorphic modular forms of level and weight , that is, correlations between their root numbers and Hecke…
Studying number theory with deep learning: a case study with the Möbius and squarefree indicator functions
David Lowry-Duda
Building on work of Charton, we train small transformer models to calculate the Möbius function and the squarefree indicator function . The models attain nontrivi…
On Murmurations and Trace Formulas
David Lowry-Duda
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 a…
Learning Fricke signs from Maass form Coefficients
Joanna Bieri, Giorgi Butbaia, Edgar Costa +6
In this paper, we conduct a data-scientific investigation of Maass forms. We find that averaging the Fourier coefficients of Maass forms with the same Fricke sign reveals patterns…
Machine learning the vanishing order of rational L-functions
Joanna Bieri, Giorgi Butbaia, Edgar Costa +6
In this paper, we study the vanishing order of rational -functions from a data scientific perspective. Each -function is represented in our data by finitely many Dirichlet co…
Learning Euler Factors of Elliptic Curves
Angelica Babei, François Charton, Edgar Costa +5
We apply transformer models and feedforward neural networks to predict Frobenius traces from elliptic curves given other traces . We train further models to predict $a_p…