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arXiv · 2607.15998

Upper bounds for moments of analytic ranks of elliptic curves over number fields

Tristan Phillips·Saahil Sharma
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Abstract

We prove a conditional upper bound for moments of the analytic rank of elliptic curves over number fields. We also prove conditional bounds for the density of elliptic curves with analytic rank larger than a given bound.

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Tristan Phillips, Saahil Sharma. 2026-07-17. Upper bounds for moments of analytic ranks of elliptic curves over number fields. https://arxiv.org/abs/2607.15998

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