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2006 Random Matrix Theory and the Fourier Coefficients of Half-Integral-Weight Forms
J.B. Conrey, J. P. Keating, M. O. Rubenstein, N. C. Snaith
Experiment. Math. 15(1): 67-82 (2006).


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.


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J.B. Conrey. J. P. Keating. M. O. Rubenstein. N. C. Snaith. "Random Matrix Theory and the Fourier Coefficients of Half-Integral-Weight Forms." Experiment. Math. 15 (1) 67 - 82, 2006.


Published: 2006
First available in Project Euclid: 16 June 2006

zbMATH: 1144.11035
MathSciNet: MR2229387

Primary: 11M , 15A52

Keywords: half-integral weight form , L-functions, elliptic curve , Random matrix theory

Rights: Copyright © 2006 A K Peters, Ltd.


Vol.15 • No. 1 • 2006
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