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Congruence
class bias and the Lang–Trotter conjecture for families of
elliptic curves
Seraphim Jarov, Alex Khadra and Nahid Walji |
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Vol. 17 (2024), No. 4, 569–592
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Abstract |
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For various families of elliptic curves over the integers, we obtain distribution results towards the Lang–Trotter conjecture on average. We demonstrate the existence of a congruence class bias in this context, and then investigate this further computationally. |
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Keywords
elliptic curves, traces of Frobenius, Lang–Trotter
conjecture
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Mathematical Subject Classification
Primary: 11G05, 14H52
Secondary: 11N37
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Milestones
Received: 4 April 2022
Revised: 9 May 2023
Accepted: 15 May 2023
Published: 2 October 2024
Communicated by Bjorn Poonen
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Authors |
| Seraphim Jarov | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| Alex Khadra | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| Nahid Walji | |
| Department of Mathematics University of British Columbia Vancouver, BC Canada |
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| © 2024 MSP (Mathematical Sciences Publishers). |
