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Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(online) ISSN 0273-0979(print)

 

Lang-Trotter revisited


Author: Nicholas M. Katz
Journal: Bull. Amer. Math. Soc. 46 (2009), 413-457
MSC (2000): Primary 11F80, 11G05, 14G35
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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Additional Information

Nicholas M. Katz
Affiliation: Department of Mathematics, Fine Hall, Princeton University, Princeton, New Jersey 08544-1000
Email: nmk@math.princeton.edu

DOI: http://dx.doi.org/10.1090/S0273-0979-09-01257-9
PII: S 0273-0979(09)01257-9
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.