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Rank bias for
elliptic curves mod $p$
Kimball Martin and Thomas Pharis
Vol. 15 (2022), No. 4, 709–726
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Abstract |
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We conjecture that, for a fixed prime , rational elliptic curves with higher rank tend to have more points mod . We show that there is an analogous bias for modular forms with respect to root numbers, and conjecture that the order of the rank bias for elliptic curves is greater than that of the root number bias for modular forms. |
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Keywords
elliptic curves, ranks, counting points mod $p$, modular
forms, root numbers, Fourier coefficients
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Mathematical Subject Classification
Primary: 11F11, 11F30, 11G05
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Milestones
Received: 10 December 2021
Revised: 5 January 2022
Accepted: 6 January 2022
Published: 7 January 2023
Communicated by Ken Ono
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Authors |
| Kimball Martin | |
| Department of Mathematics University of Oklahoma Norman, OK United States |
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| Thomas Pharis | |
| Department of Mathematics Indiana University Bloomington, IN United States |
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