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arXiv · 2312.05817

The average analytic rank of elliptic curves with prescribed level structure

Peter J. Cho·Keunyoung Jeong·Junyeong Park
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Abstract

Assuming the Hasse--Weil conjecture and the generalized Riemann hypothesis for the $L$-functions of the elliptic curve, we give an upper bound of the average analytic rank of elliptic curves over the number field with a level structure such that the corresponding compactified moduli stack is representable by the projective line.

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Peter J. Cho, Keunyoung Jeong, Junyeong Park. 2023-12-10. The average analytic rank of elliptic curves with prescribed level structure. https://arxiv.org/abs/2312.05817

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