Power moments of automorphic L-functions related to Maass forms for SL3(ℤ)
Let ff be a self-dual Hecke-Maass eigenform for the group SL3(Z)S{L}_{3}\left({\mathbb{Z}}). For 12<σ<1\frac{1}{2}\lt \sigma \lt 1 fixed we define m(σ)m\left(\sigma ) (≥2\ge 2) as the supremum of all numbers mm such that ∫1T∣L(s,f)∣mdt≪f,εT1+ε,\underset{1}{\overset{T}{\int }}| L\left(s,f){| }^...
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | article |
| Lenguaje: | EN |
| Publicado: |
De Gruyter
2021
|
| Materias: | |
| Acceso en línea: | https://doaj.org/article/90fa483de27e426b9ec3a54470494d80 |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| id |
oai:doaj.org-article:90fa483de27e426b9ec3a54470494d80 |
|---|---|
| record_format |
dspace |
| spelling |
oai:doaj.org-article:90fa483de27e426b9ec3a54470494d802021-12-05T14:10:53ZPower moments of automorphic L-functions related to Maass forms for SL3(ℤ)2391-545510.1515/math-2021-0076https://doaj.org/article/90fa483de27e426b9ec3a54470494d802021-08-01T00:00:00Zhttps://doi.org/10.1515/math-2021-0076https://doaj.org/toc/2391-5455Let ff be a self-dual Hecke-Maass eigenform for the group SL3(Z)S{L}_{3}\left({\mathbb{Z}}). For 12<σ<1\frac{1}{2}\lt \sigma \lt 1 fixed we define m(σ)m\left(\sigma ) (≥2\ge 2) as the supremum of all numbers mm such that ∫1T∣L(s,f)∣mdt≪f,εT1+ε,\underset{1}{\overset{T}{\int }}| L\left(s,f){| }^{m}{\rm{d}}t{\ll }_{f,\varepsilon }{T}^{1+\varepsilon }, where L(s,f)L\left(s,f) is the Godement-Jacquet L-function related to ff. In this paper, we first show the lower bound of m(σ)m\left(\sigma ) for 23<σ<1\frac{2}{3}\lt \sigma \lt 1. Then we establish asymptotic formulas for the second, fourth and sixth powers of L(s,f)L\left(s,f) as applications.Huang JingLiu HuafengZhang DeyuDe Gruyterarticlepower momentsl-functionautomorphic form11f0311f66MathematicsQA1-939ENOpen Mathematics, Vol 19, Iss 1, Pp 1007-1017 (2021) |
| institution |
DOAJ |
| collection |
DOAJ |
| language |
EN |
| topic |
power moments l-function automorphic form 11f03 11f66 Mathematics QA1-939 |
| spellingShingle |
power moments l-function automorphic form 11f03 11f66 Mathematics QA1-939 Huang Jing Liu Huafeng Zhang Deyu Power moments of automorphic L-functions related to Maass forms for SL3(ℤ) |
| description |
Let ff be a self-dual Hecke-Maass eigenform for the group SL3(Z)S{L}_{3}\left({\mathbb{Z}}). For 12<σ<1\frac{1}{2}\lt \sigma \lt 1 fixed we define m(σ)m\left(\sigma ) (≥2\ge 2) as the supremum of all numbers mm such that ∫1T∣L(s,f)∣mdt≪f,εT1+ε,\underset{1}{\overset{T}{\int }}| L\left(s,f){| }^{m}{\rm{d}}t{\ll }_{f,\varepsilon }{T}^{1+\varepsilon }, where L(s,f)L\left(s,f) is the Godement-Jacquet L-function related to ff. In this paper, we first show the lower bound of m(σ)m\left(\sigma ) for 23<σ<1\frac{2}{3}\lt \sigma \lt 1. Then we establish asymptotic formulas for the second, fourth and sixth powers of L(s,f)L\left(s,f) as applications. |
| format |
article |
| author |
Huang Jing Liu Huafeng Zhang Deyu |
| author_facet |
Huang Jing Liu Huafeng Zhang Deyu |
| author_sort |
Huang Jing |
| title |
Power moments of automorphic L-functions related to Maass forms for SL3(ℤ) |
| title_short |
Power moments of automorphic L-functions related to Maass forms for SL3(ℤ) |
| title_full |
Power moments of automorphic L-functions related to Maass forms for SL3(ℤ) |
| title_fullStr |
Power moments of automorphic L-functions related to Maass forms for SL3(ℤ) |
| title_full_unstemmed |
Power moments of automorphic L-functions related to Maass forms for SL3(ℤ) |
| title_sort |
power moments of automorphic l-functions related to maass forms for sl3(ℤ) |
| publisher |
De Gruyter |
| publishDate |
2021 |
| url |
https://doaj.org/article/90fa483de27e426b9ec3a54470494d80 |
| work_keys_str_mv |
AT huangjing powermomentsofautomorphiclfunctionsrelatedtomaassformsforsl3z AT liuhuafeng powermomentsofautomorphiclfunctionsrelatedtomaassformsforsl3z AT zhangdeyu powermomentsofautomorphiclfunctionsrelatedtomaassformsforsl3z |
| _version_ |
1718371616256163840 |