The fourth moment of truncated Eisenstein series

Autor:	Djanković, Goran, Khan, Rizwanur
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Primary: 11F12 11M99 Secondary: 81Q50 58J51
Druh dokumentu:	Working Paper
Popis:	We obtain an asymptotic for the fourth moment of truncated Eisenstein series of large Laplacian eigenvalue, verifying for the first time that the main term corresponds to Gaussian random behavior. This is a manifestation of the Random Wave Conjecture, which for Eisenstein series was formulated by Hejhal and Rackner over thirty years ago. Our innovation is to tackle the problem after introducing, at no cost, an extra averaging over the truncation parameter. Comment: 23 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2408.14815 Zobrazit plný text záznamu View this record from Arxiv