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

DOI10.1080/10586458.2006.10128953zbMATH Open1144.11035DBLPjournals/em/ConreyKRS06arXivmath/0412083OpenAlexW1999409063WikidataQ102399689 ScholiaQ102399689MaRDI QIDQ3413599

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Publication date: 13 December 2006

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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 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.

Full work available at URL: https://arxiv.org/abs/math/0412083

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