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)peer-review

16 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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