Name
Title | ||
|---|---|---|
The Sato-Tate Distribution and the Values of Fourier Coefficients of Modular Newforms. |
Abstract | ||
|---|---|---|
The Sato-Tate conjecture has been recently settled in great generality. One natural question now concerns the rate of convergence of the distribution of the Fourier coefficients of modular newforms to the Sato-Tate distribution. In this paper, we address this issue, imposing congruence conditions on the primes and on the Fourier coefficients as well. Assuming a proper error term in the convergence to a conjectural limiting distribution, supported by experimental data, we prove the Lang-Trotter conjecture, and in the direction of Lehmer's conjecture, we prove that tau(p) = 0 has at most finitely many solutions. In fact, we propose a conjecture, much more general than Lehmer's, about the vanishing of Fourier coefficients of any modular newform. |
Year | DOI | Venue |
|---|---|---|
2012 | 10.1080/10586458.2011.611747 | EXPERIMENTAL MATHEMATICS |
Keywords | Field | DocType |
Sato-Tate distribution,Lang-Trotter conjecture,Lehmer's conjecture | Convergence (routing),Topology,Sato–Tate conjecture,Mathematical analysis,Fourier series,Rate of convergence,Congruence (geometry),Conjecture,Mathematics,Asymptotic distribution,Lehmer's conjecture | Journal |
Volume | Issue | ISSN |
21.0 | 1.0 | 1058-6458 |
Citations | PageRank | References |
1 | 0.63 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Josep González | 1 | 17 | 4.49 |
| Jorge Jimenez Urroz | 2 | 27 | 3.65 |