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

Original language | English |

Pages (from-to) | 67 - 82 |

Number of pages | 16 |

Journal | Experimental Mathematics |

Volume | 15 (1) |

Publication status | Published - Jan 2006 |

### Bibliographical note

Publisher: A K Peters LtdOther identifier: IDS number 050LK

## Fingerprint Dive into the research topics of 'Random matrix theory and the Fourier coefficients of half-integral weight forms'. Together they form a unique fingerprint.

## Cite this

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