Xing, Chaoping; Niederreiter, Harald Drinfeld modules of rank 1 and algebraic curves with many rational points. (English) Zbl 0982.11034 Monatsh. Math. 127, No. 3, 219-241 (1999). 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. Reviewer: D.Goss (Columbus/Ohio) Cited in 1 Review 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.) Keywords:algebraic curves over finite fields; large numbers of rational points; Drinfeld modules; abelian reciprocity laws PDFBibTeX XMLCite \textit{C. Xing} and \textit{H. Niederreiter}, Monatsh. Math. 127, No. 3, 219--241 (1999; Zbl 0982.11034) Full Text: DOI Online Encyclopedia of Integer Sequences: Maximal number of rational points on a curve of genus n over GF(2).