Abstract
We give improved uniform estimates for the rate of convergence to Plancherel measure of Hecke eigenvalues of holomorphic forms of weight 2 and level N. These are applied to determine the sharp cutoff for the non-backtracking random walk on arithmetic Ramanujan graphs and to Serre’s problem of bounding the multiplicities of modular forms whose coefficients lie in number fields of degree d.
Original language | English (US) |
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Pages (from-to) | 191-213 |
Number of pages | 23 |
Journal | Acta Arithmetica |
Volume | 214 |
DOIs | |
State | Published - 2024 |
Externally published | Yes |
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
Keywords
- Hecke eigenvalues
- Plancherel measure
- eigenvalue distribution
- modular curve