Supersingular distribution on average for congruence classes of primes

Abstract

We demonstrate the existence of a congruence class bias in the distribution of supersingular primes on average for elliptic curves over $\Q$. For example, we show that on average there are twice as many supersingular primes congruent to 2 mod 3 as there are congruent to 1 mod 3. Our result is obtained using the averaging approach of Fouvry-Murty along with ideas of David-Pappalardi.

Preprint of an old paper

References in corpus (1)

• Supersingular primes for points on $X_0(p)/w_p$

Cited by in corpus (1)

• On the distribution of traces of Frobenius for families of elliptic curves and the Lang-Trotter conjecture on average