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

Igor E. Shparlinski*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Citations (Scopus)

Abstract

We show that the reductions modulo primes p ≤ x of the elliptic curve Ea,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 languageEnglish
Pages (from-to)647-664
Number of pages18
JournalForum Mathematicum
Volume25
Issue number3
DOIs
Publication statusPublished - May 2013

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