### 29 juni 2007, kl 13.15-14.15, KTH, sal 3721.

### Nathan Jones (Centre de Recherches Mathematiques,
Universite de Montreal):
The square-free sieve and elliptic curve constants

**Abstract.**
Let E be an elliptic curve defined over the rational numbers. For a prime
p of good
reduction for E, let E_p denote
the reduction of E modulo p. There are many conjectures
which give precise asymptotics for functions which count
the number of primes p up to x for
which E_p has some desired property (e.g. its number of points is prime,
or is
equal to
p+1-r for a fixed integer r). In this talk I will use a square-free sieve
of Hooley
to study
the constants
appearing in these asymptotic formulas.