The Square Sieve and the Lang-Trotter Conjecture

@inproceedings{Cojocaru2001TheSS,
  title={The Square Sieve and the Lang-Trotter Conjecture},
  author={Alina Carmen Cojocaru and Ram Murty},
  year={2001}
}
1 Let E be an elliptic curve defined over Q and without complex multiplication. Let K be a fixed imaginary quadratic field. We find nontrivial upper bounds for the number of ordinary primes p ≤ x for which Q(πp) = K, where πp denotes the Frobenius endomorphism of E at p. More precisely, under a certain generalized Riemann hypothesis we show that this number is OE ( x 17 18 log x ) , and unconditionally we show that this number is OE,K ( x(log log x) 13 12 (log x) 25 24 ) . We also prove that… CONTINUE READING
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References

Publications referenced by this paper.
Showing 1-10 of 22 references

Frobenius distributions in GL2-extensions

  • S. Lang, H. Trotter
  • Lecture Notes in Mathematics 504, Springer Verlag
  • 1976
Highly Influential
7 Excerpts

An introduction to Artin L-functions

  • M. Ram Murty
  • J. Ramanujan Math. Soc
  • 2001

Murty and N . Saradha , Modular forms and the Chebotarev density theorem

  • V. Kumar Murty, V. Kumar
  • Amer . J . Math .
  • 2001

A course in arithmetic

  • J-P. Serre
  • Graduate texts in mathematics 7, Springer Verlag
  • 1996

On the distribution of supersingular primes

  • E. Fouvry, M. Ram Murty
  • Canadian Journal of Math
  • 1996

Supersingular primes common to two elliptic curves”, London Mathematical Society Lecture Notes Series 215, Number Theory, Paris 199293

  • E. Fouvry, M. Ram Murty
  • (ed. Sinnou David),
  • 1995

Advanced topics in the arithmetic of elliptic curves

  • J. H. Silverman
  • Graduate Texts in Mathematics 151, Springer…
  • 1994

, N . Saradha , “ Modular forms and the Chebotarev density theorem ”

  • V. Kumar Murty Ram Murty
  • Amer . J . Math .
  • 1988

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