On the splitting rate of rate of a tower of Artin-Schreier type
Vol. 44 No. 173 (2020), Mathematics
Vol. 44 No. 173 (2020)

On the splitting rate of rate of a tower of Artin-Schreier type

Mathematics
https://doi.org/10.18257/raccefyn.1140
Published 2020-12-07
Horacio Navarro
Departamento de Matemáticas, Universidad del Valle, Cali, Colombia
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How to Cite

Navarro, H. (2020). On the splitting rate of rate of a tower of Artin-Schreier type. Revista De La Academia Colombiana De Ciencias Exactas, Físicas Y Naturales, 44(173), 1167–1173. https://doi.org/10.18257/raccefyn.1140
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Abstract

In this note we study the asymptotic behaviour of the number of rational places in a tower of function fields of Artin-Schreier type over a finite field with 2s elements, where s > 0 is an odd integer.

https://doi.org/10.18257/raccefyn.1140

Keywords

Towers of function fields | Splitting rate | Asymptotic behaviour | Number of rational places
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References

Beelen, P., Garcia, A., & Stichtenoth, H. (2004). On towers of function fields of Artin-Schreier type. Bulletin of the Brazilian Mathematical Society, 35(2), 151–164.

Beelen, P., Garcia, A., & Stichtenoth, H. (2006). Towards a classification of recursive towers of function fields over finite fields. Finite Fields and Their Applications, 12(1), 56–77.

Chara, M., Navarro, H., & Toledano, R. (2018). A problem of Beelen, Garcia and Stichtenoth on an Artin-Schreier tower in characteristic two. Acta Arithmetica, 182(), 311–330.

Chara, M., & Toledano, R. (2015). Asymptotically bad towers of function fields. Tokyo Journal of Mathematics, 38(2), 339–352.

Drinfel’d, V., & Vladut, S. (1983). Number of points of an algebraic curve. Functional Analysis and its Applications, 17(1), 53–54.

Garcia, A., & Stichtenoth, H. (1995). A tower of Artin-Schreier extensions of function fields attaining the drinfeld-vladut bound. Inventiones Mathematicae, 121(1), 211–222.

Garcia, A.,&Stichtenoth, H. (2000). Skew pyramids of function fields are asymptotically bad. In Coding theory, cryptography and related areas (pp. 111–113). Springer.

Ihara, Y. (1981). Some remarks on the number of rational points of algebraic curves over finite fields. J. Fac. Sci. Univ. Tokyo Sect. IA Math., 28(3), 721–724 (1982).

Ling, S., Stichtenoth, H., & Yang, S. (2005). A class of artin-schreier towers with finite genus. Bulletin of the Brazilian Mathematical Society, 36(3), 393–401.

Serre, J.-P. (1983). Sur le nombre des points rationnels d’une courbe alg´ebrique sur un corps fini. CR Acad. Sci. Paris, 296(Serie I), 397–402.

Stichtenoth, H. (2009). Algebraic function fields and codes (Vol. 254). Berlin: Springer-Verlag.

Tsfasman, M. A., Vladut, S., & Zink, T. (1982). Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound. Mathematische Nachrichten,109(1), 21–28.

Weil, A. (1948). Sur les courbes alg´ebriques et les vari´et´es qui s’en d´eduisent (No. 1041).Hermann.

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