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arXiv · 1004.2753

Effective equidistribution and the Sato-Tate law for families of elliptic curves

Steven J. Miller·M. Ram Murty
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Abstract

Extending recent work of others, we provide effective bounds on the family of all elliptic curves and one-parameter families of elliptic curves modulo p (for p prime tending to infinity) obeying the Sato-Tate Law. We present two methods of proof. Both use the framework of Murty-Sinha; the first involves only knowledge of the moments of the Fourier coefficients of the L-functions and combinatorics, and saves a logarithm, while the second requires a Sato-Tate law. Our purpose is to illustrate how the caliber of the result depends on the error terms of the inputs and what combinatorics must be done.

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Steven J. Miller, M. Ram Murty. 2010-04-30. Effective equidistribution and the Sato-Tate law for families of elliptic curves. https://doi.org/10.1016/j.jnt.2010.06.013

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