## Experimental Mathematics

- Experiment. Math.
- Volume 15, Number 1 (2006), 67-82.

### Random Matrix Theory and the Fourier Coefficients of Half-Integral-Weight Forms

J.B. Conrey, J. P. Keating, M. O. Rubenstein, and N. C. Snaith

#### 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 center of the critical strip are used to motivate a series of conjectures 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.

#### Article information

**Source**

Experiment. Math., Volume 15, Number 1 (2006), 67-82.

**Dates**

First available in Project Euclid: 16 June 2006

**Permanent link to this document**

https://projecteuclid.org/euclid.em/1150476905

**Mathematical Reviews number (MathSciNet)**

MR2229387

**Zentralblatt MATH identifier**

1144.11035

**Keywords**

L-functions, elliptic curve random matrix theory half-integral weight form

#### Citation

Conrey, J.B.; Keating, J. P.; Rubenstein, M. O.; Snaith, N. C. Random Matrix Theory and the Fourier Coefficients of Half-Integral-Weight Forms. Experiment. Math. 15 (2006), no. 1, 67--82. https://projecteuclid.org/euclid.em/1150476905