• Corpus ID: 233872721

Chebotarev Density Theorem and Extremal Primes for non-CM elliptic curves

  title={Chebotarev Density Theorem and Extremal Primes for non-CM elliptic curves},
  author={Amita Malik and Neha Prabhu},
Abstract. For a fixed non-CM elliptic curve E over Q and a prime l, we prove an asymptotic formula on the number of primes p ≤ x for which the Frobenius trace ap(E) satisfies the congruence ap(E) ≡ [2 √ p] (mod l). In order to achieve this, we establish a joint distribution concerning the fractional part of αp for θ ∈ [0, 1], α > 0, and primes p satisfying the Chebotarev condition. As a corollary, we also obtain upper bounds for the number of extremal primes. The results rely on GRH for… 


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