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.
- Publication:
-
Acta Arithmetica
- Pub Date:
- 2010
- DOI:
- 10.4064/aa142-4-7
- arXiv:
- arXiv:1307.5346
- Bibcode:
- 2010AcAri.142..387W
- Keywords:
-
- Mathematics - Number Theory;
- 11G05;
- 14H52
- E-Print:
- Preprint of an old paper