Learning Fricke signs from Maass form coefficients
Abstract
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 analogous to the recently discovered "murmuration" phenomenon, and that these patterns become more pronounced when parity is incorporated as an additional feature. Approximately $43\%$ of the forms in our dataset have an unknown Fricke sign. For the remaining forms, we employ Linear Discriminant Analysis (LDA) to machine learn their Fricke sign, achieving $96\%$ (resp. $94\%$) accuracy for forms with even (resp. odd) parity.
Fields of Study & Subjects
Non-Destructive Testing Techniques
Ultrasonics and Acoustic Wave Propagation
Neural Networks and Applications
Publication details
- Journal / source
- Advances in Theoretical and Mathematical Physics
- Volume
- 29
- Issue
- 8
- Pages
- 2403–2423
- Publication date
- 1 January 2026
- Language
- EN