On a Question of Zannier

Abstract

We formulate and answer a question of Zannier about elliptic curves over varying prime fields. We then give some experimental findings. In a final section, we formulate some analogous questions for curves of higher genus.

Keywords:

• elliptic curves
• Cartier operator
• equidistribution
• Eisenstein series

AMS Subject Classification:

• 11G05
• 11K99
• 14G15
• 14H10
• 14H52

Disclosure statement

No potential conflict of interest was reported by the author.