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Drinfeld modules of rank 1 and algebraic curves with many rational points. (English) Zbl 0982.11034

Let \(\mathbb{F}_p\) be the base finite field with \(p\) elements, \(p\) prime. Algebraic curves with large numbers of rational points with respect to the genus are of great utility. In the paper being reviewed, the authors construct such curves through the use of Drinfeld modules of rank one and their connection to abelian reciprocity laws.

MSC:

11G09 Drinfel’d modules; higher-dimensional motives, etc.
11G20 Curves over finite and local fields
11R58 Arithmetic theory of algebraic function fields
14G15 Finite ground fields in algebraic geometry
14H05 Algebraic functions and function fields in algebraic geometry
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory
11R60 Cyclotomic function fields (class groups, Bernoulli objects, etc.)
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