On the Sato-Tate conjecture on average for some families of elliptic curves

Igor E. Shparlinski

doi:10.1515/FORM.2011.141

On the Sato-Tate conjecture on average for some families of elliptic curves

Igor E. Shparlinski^*

^*Corresponding author for this work

School of Computing

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

Abstract

We show that the reductions modulo primes p ≤ x of the elliptic curve E_a,b : Y² = X³ + aX + b behave as predicted by the Sato-Tate conjecture, on average over integers a and b such that a ∈ A and b ∈ B where one of the sets A, B ⊆ ℤ is a centered at the origin interval and the other set is of a rather general structure. These asymptotic formulas generalise previous results of W. D. Banks and the author, which in turn improve several previously known results.

Original language	English
Pages (from-to)	647-664
Number of pages	18
Journal	Forum Mathematicum
Volume	25
Issue number	3
DOIs	https://doi.org/10.1515/FORM.2011.141
Publication status	Published - May 2013

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10.1515/FORM.2011.141

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On the Sato-Tate conjecture on average for some families of elliptic curves

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