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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Lang-Trotter revisited
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by Nicholas M. Katz PDF
Bull. Amer. Math. Soc. 46 (2009), 413-457 Request permission

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

  • Dedicated: Dedicated to the memory of Serge Lang
  • © 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