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On the Sato–Tate conjecture on average for some families of elliptic curves
-
Igor E. Shparlinski
Published/Copyright:
May 2, 2013
Abstract.
We show that the reductions modulo primes 
of the elliptic curve
behave as predicted by the Sato–Tate conjecture, on average over
integers a and b such that 
and 
where one of the sets 
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.
Received: 2009-11-03
Revised: 2011-06-16
Published Online: 2013-05-02
Published in Print: 2013-05-01
© 2013 by Walter de Gruyter Berlin Boston
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Articles in the same Issue
- Masthead
- Low-dimensional non-abelian Leibniz cohomology
- Twisted torsion invariants and link concordance
- Groups with faithful irreducible projective unitary representations
- Universality of the Selberg zeta-function for the modular group
- An innocent theorem of Banaschewski, applied to an unsuspecting theorem of De Marco, and the aftermath thereof
- Knotted surfaces in 4-manifolds
- Knot surgery and Scharlemann manifolds
- On the Sato–Tate conjecture on average for some families of elliptic curves
