A conjecture for the regularized fourth moment of Eisenstein series

Goran Djanković, Rizwanur Khan

Research output: Contribution to journalArticle

2 Citations (Scopus)


We formulate a version of the Random Wave Conjecture for the fourth moment of Eisenstein series which is based on Zagier's regularized inner product. We prove an asymptotic formula expressing the regularized fourth moment as a mean value of L-functions. This is an advantage over previous work in the literature, which has approached the fourth moment problem through truncated Eisenstein series and not yielded a suitable expression in terms of L-functions.

Original languageEnglish
Pages (from-to)236-257
Number of pages22
JournalJournal of Number Theory
Publication statusPublished - 1 Jan 2018



  • Automorphic forms
  • Eisenstein series
  • Equidistribution
  • L-functions
  • L-norm
  • Quantum chaos
  • Random wave conjecture
  • Regularized inner products

ASJC Scopus subject areas

  • Algebra and Number Theory

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