The sixth and eighth moments of Fourier coefficients of cusp forms (Q841261)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The sixth and eighth moments of Fourier coefficients of cusp forms |
scientific article; zbMATH DE number 5604003
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The sixth and eighth moments of Fourier coefficients of cusp forms |
scientific article; zbMATH DE number 5604003 |
Statements
The sixth and eighth moments of Fourier coefficients of cusp forms (English)
0 references
15 September 2009
0 references
In this paper, the author considered the sixth and eighth moments of the Hecke eigenvalues of a holomorphic eigencusp form and proved the following asymptotic formula \[ \sum_{n\leq x} \lambda_f(n)^\ell = xP_\ell(x) + O_{f, \varepsilon}(x^{\theta_\ell+\varepsilon}), \] for \(\ell=6, 8\), where \(\varepsilon\) is an arbitrarily small positive number, \(P_6(t), P_8(t)\) are polynomials of degree 4, 13 respectively and \(\theta_6=31/32\theta_8=127/128\).
0 references
Fourier coefficients of cusp forms
0 references
symmetric power \(L\)-function
0 references
0 references
