Uniform approximate functional equation for principal L-functions
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2001
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866913578927259648 |
|---|---|
| author | Harcos, Gergely |
| author_facet | Harcos, Gergely |
| contents | We prove an approximate functional equation for the central value of the L-series attached to an irreducible cuspidal automorphic representation of GL(m) over a number field with unitary central character. We investigate the decay rate of the terms involved using the analytic conductor of Iwaniec and Sarnak as a guideline. Straightforward extensions of the results exist for products of central values. We hope that these formulae will help further understanding of the central values of principal L-functions, such as finding good bounds on their various power means, or establishing subconvexity or nonvanishing results in certain families. A crucial role in the proofs is played by recent progress on the Ramanujan--Selberg conjectures achieved by Luo, Rudnick and Sarnak. The bounds at the non-Archimedean places enter through the work of Molteni. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_math_0111312 |
| institution | arXiv |
| publishDate | 2001 |
| record_format | arxiv |
| spellingShingle | Uniform approximate functional equation for principal L-functions Harcos, Gergely Number Theory 11M41, 11F66 We prove an approximate functional equation for the central value of the L-series attached to an irreducible cuspidal automorphic representation of GL(m) over a number field with unitary central character. We investigate the decay rate of the terms involved using the analytic conductor of Iwaniec and Sarnak as a guideline. Straightforward extensions of the results exist for products of central values. We hope that these formulae will help further understanding of the central values of principal L-functions, such as finding good bounds on their various power means, or establishing subconvexity or nonvanishing results in certain families. A crucial role in the proofs is played by recent progress on the Ramanujan--Selberg conjectures achieved by Luo, Rudnick and Sarnak. The bounds at the non-Archimedean places enter through the work of Molteni. |
| title | Uniform approximate functional equation for principal L-functions |
| topic | Number Theory 11M41, 11F66 |
| url | https://arxiv.org/abs/math/0111312 |