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

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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.
28 pages, 8 figures

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Number Theory, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/100968

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0412083
 http://arxiv.org/abs/math/0412083

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arXiv