Lang-Trotter Revisited

Nicholas M. Katz

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

Lang-Trotter Revisited

Nicholas M. Katz

Mathematics

Research output: Contribution to journal › Article › peer-review

17 Scopus citations

Abstract

The Lang-Trotter Conjecture(s) concern elliptic curves over the field Q{double-struck} 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.

Original language	English (US)
Pages (from-to)	413-457
Number of pages	45
Journal	Bulletin of the American Mathematical Society
Volume	46
Issue number	3
DOIs	https://doi.org/10.1090/S0273-0979-09-01257-9
State	Published - Jul 2009

All Science Journal Classification (ASJC) codes

General Mathematics
Applied Mathematics

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10.1090/S0273-0979-09-01257-9

Cite this

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AB - The Lang-Trotter Conjecture(s) concern elliptic curves over the field Q{double-struck} 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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ER -

Lang-Trotter Revisited

Abstract

All Science Journal Classification (ASJC) codes

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