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

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

2004-12-03

arxiv.org/abs/math/0412083v4

Mathematics

Number Theory

28 pages, 8 figures

Scientific paper

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 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.

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