Kwan, Chung-Hang;
(2024)
Spectral Moment Formulae for GL(3) × GL(2) L-functions I: The Cuspidal Case.
Algebra and Number Theory
, 18
(10)
pp. 1817-1862.
10.2140/ant.2024.18.1817.
(In press).
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Abstract
Spectral moment formulae of various shapes have proven very successful in studying the statistics of central L-values. We establish, in a completely explicit fashion, such formulae for the family of GL(3) × GL(2) Rankin–Selberg L-functions using the period integral method. Our argument does not rely on either the Kuznetsov or Voronoi formulae. We also prove the essential analytic properties and derive explicit formulae for the integral transform of our moment formulae. We hope that our method will provide deeper insights into moments of L-functions for higher-rank groups.
| Type: | Article |
|---|---|
| Title: | Spectral Moment Formulae for GL(3) × GL(2) L-functions I: The Cuspidal Case |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.2140/ant.2024.18.1817 |
| Publisher version: | http://dx.doi.org/10.2140/ant.2024.18.1817 |
| Language: | English |
| Additional information: | This work is licensed under a Creative Commons License. The images or other third-party material in this article are included in the Creative Commons license, unless indicated otherwise in the credit line; if the material is not included under the Creative Commons license, users will need to obtain permission from the license holder to reproduce the material. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/ |
| Keywords: | Science & Technology, Physical Sciences, Mathematics, automorphic forms, automorphic L-functions, Maass forms, moments of L-functions, Rankin-Selberg L-functions, period integrals, Whittaker functions, hypergeometric functions, Poincare series, SELBERG L-FUNCTIONS, TWISTED L-FUNCTIONS, SUBCONVEXITY PROBLEM, AUTOMORPHIC-FORMS, SERIES, WEYL, TRANSFORMS, KUZNETSOV, WEIGHT, BOUNDS |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10200843 |
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