Lang-Trotter revisited
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- by Nicholas M. Katz PDF
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Abstract:
The Lang–Trotter Conjecture(s) concern elliptic curves over the field $\mathbb {Q}$ of rational numbers. We first explain the broader number-theoretic context into which they fit. Then we turn to formulating their “function field” analogues. We explain how these analogues can be proven in some very special cases, and we speculate about what might be true in the general function field case.References
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Additional Information
- Nicholas M. Katz
- Affiliation: Department of Mathematics, Fine Hall, Princeton University, Princeton, New Jersey 08544-1000
- MR Author ID: 99205
- ORCID: 0000-0001-9428-6844
- Email: nmk@math.princeton.edu
- Received by editor(s): December 21, 2008
- Received by editor(s) in revised form: February 23, 2009
- Published electronically: March 27, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Bull. Amer. Math. Soc. 46 (2009), 413-457
- MSC (2000): Primary 11F80, 11G05, 14G35
- DOI: https://doi.org/10.1090/S0273-0979-09-01257-9
- MathSciNet review: 2507277
Dedicated: Dedicated to the memory of Serge Lang