Turkish Journal of Mathematics
DOI
10.3906/mat-1411-42
Abstract
Let $\FF=(F_n)_{n\geq 0}$ be a quadratic recursive tower of algebraic function fields over the finite field $\F_2$, i.e. $\FF$ is a recursive tower such that $[F_n:F_{n-1}]=2$ for all $n\geq 1$. For any integer $r\geq 1$, let $\beta_r(\FF):=\lim_{n\to \infty} B_r(F_n)/g(F_n)$, where $B_r(F_n)$ is the number of places of degree $r$ and $g(F_n)$ is the genus, respectively, of $F_n/\F_2$. In this paper we give a classification of all rational functions $f(X,Y)\in \F_2(X,Y)$ that may define a quadratic recursive tower $\FF$ over $\F_2$ with at least one positive invariant $\beta_r(\FF)$. Moreover, we estimate $\beta_1(\FF)$ for each such tower.
Keywords
Towers of algebraic function fields, genus, number of places
First Page
665
Last Page
682
Recommended Citation
STICHTENOTH, HENNING and TUTDERE, SEHER
(2015)
"Quadratic recursive towers of function fields over $\mathbb{F}_2$,"
Turkish Journal of Mathematics: Vol. 39:
No.
5, Article 6.
https://doi.org/10.3906/mat-1411-42
Available at:
https://journals.tubitak.gov.tr/math/vol39/iss5/6
