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.
Publié le : 2006-05-14
Classification:
L-functions, elliptic curve,
random matrix theory,
half-integral weight form,
11M,
15A52
@article{1150476905,
author = {Conrey, J.B. and Keating, J. P. and Rubenstein, M. O. and Snaith, N. C.},
title = {Random Matrix Theory and the Fourier Coefficients of Half-Integral-Weight Forms},
journal = {Experiment. Math.},
volume = {15},
number = {1},
year = {2006},
pages = { 67-82},
language = {en},
url = {http://dml.mathdoc.fr/item/1150476905}
}
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., Tome 15 (2006) no. 1, pp. 67-82. http://gdmltest.u-ga.fr/item/1150476905/