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

Tristan Phillips, Saahil Sharma

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.

Disclosure

“results to estimate the Frobenius-trace sums that arise in the moment calculation. In Section 6, we combine these ingredients to prove Theorems 1.1 and 1.3. Acknowledgments We acknowledge the use of AI tools in the preparation of this manuscript. TP was sup- ported by the National Science Foundation, via grant DMS-2303011. 3”
PDF page 3

Classification: Drafting limited passages
Multiplier: 5
Verified: 2026-08-23T18:57:06.496907Z

Structural counts

Pages 34 pdf

Theorems 3 source

Lemmas 8 source

Propositions 7 source

Corollaries 1 source

Definitions 0 source

Displayed equations 184 source

Bibliography entries 23 source

Appendix pages 0 estimated

Count notes

Source counts use the expanded primary TeX file Moments_2026-07-14.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.