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 | References | Similar Articles | Additional Information
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.
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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
Dedicated:
Dedicated to the memory of Serge Lang
Article copyright:
© Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.