The second moment of GL3×GL2L-functions at special points
Let ϕ be a fixed Hecke–Maass form for SL3(Z) and uj traverse an orthonormal basis of Hecke–Maass forms for SL2(Z). Let 1/4+tj2 be the Laplace eigenvalue of uj. In this paper, we prove the mean Lindelöf hypothesis for the second moment of L(1/2+itj,ϕ×uj) on T<tj⩽T+T. Previously, this was proven by...
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| Vydáno v: | Mathematische annalen Ročník 393; číslo 1; s. 1429 - 1457 |
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| Hlavní autor: | |
| Médium: | Journal Article |
| Jazyk: | angličtina |
| Vydáno: |
Heidelberg
Springer Nature B.V
01.09.2025
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| Témata: | |
| ISSN: | 0025-5831, 1432-1807 |
| On-line přístup: | Získat plný text |
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| Shrnutí: | Let ϕ be a fixed Hecke–Maass form for SL3(Z) and uj traverse an orthonormal basis of Hecke–Maass forms for SL2(Z). Let 1/4+tj2 be the Laplace eigenvalue of uj. In this paper, we prove the mean Lindelöf hypothesis for the second moment of L(1/2+itj,ϕ×uj) on T<tj⩽T+T. Previously, this was proven by Young on tj⩽T. Our approach is more direct as we do not apply the Poisson summation formula to detect the ‘Eisenstein–Kloosterman’ cancellation. |
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| Bibliografie: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 14 |
| ISSN: | 0025-5831 1432-1807 |
| DOI: | 10.1007/s00208-025-03267-7 |