## Experimental Mathematics

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

#### 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

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

Mathematical Reviews number (MathSciNet)
MR2229387

Zentralblatt MATH identifier
1144.11035

Subjects
Primary: 11M 15A52

#### 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