Liberty University

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20122018

most citedSums of Euler products and statistics of elliptic curves

11 citations

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math.NT2015★ 11 cited

Sums of Euler products and statistics of elliptic curves

Chantal David, Dimitris Koukoulopoulos, Ethan Smith

We present several results related to statistics for elliptic curves over a finite field $F_{p}$ as corollaries of a general theorem about averages of Euler products that we…

math.NT2014★ 6 cited

The frequency of elliptic curve groups over prime finite fields

Vorrapan Chandee, Chantal David, Dimitris Koukoulopoulos +1

Letting $p$ vary over all primes and $E$ vary over all elliptic curves over the finite field $F_{p}$ , we study the frequency to which a given group $G$ arises as a group of…

math.NT2012★ 6 cited

Group structures of elliptic curves over finite fields

Vorrapan Chandee, Chantal David, Dimitris Koukoulopoulos +1

It is well-known that if $E$ is an elliptic curve over the finite field $F_{p}$ , then $E (F_{p}) ≃ Z / m Z \times Z / mk Z$ for some pos…

math.NT2012★ 9 cited

Averages of the number of points on elliptic curves

Greg Martin, Paul Pollack, Ethan Smith

If $E$ is an elliptic curve defined over $Q$ and $p$ is a prime of good reduction for $E$ , let $E (F_{p})$ denote the set of points on the reduced curve modulo $p$ . De…