Lang-Trotter revisited

Katz, Nicholas

doi:10.1090/S0273-0979-09-01257-9

Lang-Trotter revisited

Author: Nicholas M. Katz
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
Published electronically: March 27, 2009
MathSciNet review: 2507277
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Abstract: The Lang-Trotter Conjecture(s) concern elliptic curves over the field $\Q$ 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.

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