Random matrix theory and the Fourier coefficients of half-integral weight forms

JB Conrey, JP Keating, M Rubinstein, NC Snaith

Research output: Contribution to journalArticle (Academic Journal)

14 Citations (Scopus)

Abstract

Conjectured links between the distribution of values taken by the characteristic polynomials of random orthogonal matrices and that for certain families of L-functions at the centre of the critical strip are used to motivate a series of conjecture concerning the value-distribution of the Fourier coefficients of half-integral weight modular forms related to these L-functions. Our conjectures may be viewed as being analogous to the Sato-Tate conjecture for integral weight modular forms. Numerical evidence is presented in support of them.
Translated title of the contributionRandom matrix theory and the Fourier coefficients of half-integral weight forms
Original languageEnglish
Pages (from-to)67 - 82
Number of pages16
JournalExperimental Mathematics
Volume15 (1)
Publication statusPublished - Jan 2006

Bibliographical note

Publisher: A K Peters Ltd
Other identifier: IDS number 050LK

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