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# 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} }

- Published 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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