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 contribution||Random matrix theory and the Fourier coefficients of half-integral weight forms|
|Pages (from-to)||67 - 82|
|Number of pages||16|
|Publication status||Published - Jan 2006|
Bibliographical notePublisher: A K Peters Ltd
Other identifier: IDS number 050LK
Conrey, JB., Keating, JP., Rubinstein, M., & Snaith, NC. (2006). Random matrix theory and the Fourier coefficients of half-integral weight forms. Experimental Mathematics, 15 (1), 67 - 82. http://www.expmath.org/expmath/volumes/15/15.1/Conrey.pdf