On Towers and Composita of Towers of Function Fields over Finite Fields
نویسندگان
چکیده
منابع مشابه
Towers of Function Fields over Non-prime Finite Fields
Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(`), for ` = p with p prime and n > 3 odd. A modular interpretation of the towers is given as well.
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In this paper we construct Galois towers with good asymptotic properties over any nonprime finite field F`; i.e., we construct sequences of function fields N = (N1 ⊂ N2 ⊂ · · · ) over F` of increasing genus, such that all the extensions Ni/N1 are Galois extensions and the number of rational places of these function fields grows linearly with the genus. The limits of the towers satisfy the same ...
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Let F Fl be an algebraic function field of one variable, whose constant field is the finite field of cardinality l. Weil's theorem states that the number N=N(F ) of places of degree one of F Fl satisfies the estimate N l+1+2g l , (0.1) where g= g(F ) denotes the genus of F. It is well known that for g large with respect to l, the Weil bound (0.1) is not optimal; see [5, 9]. Drinfeld and Vladut ...
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We consider a tower of function fields F = (Fn)n≥0 over a finite field Fq and a finite extension E/F0 such that the sequence E := E ·F = (EFn)n≥0 is a tower over the field Fq. Then we deal with the following: What can we say about the invariants of E ; i.e., the asymptotic number of the places of degree r for any r ≥ 1 in E , if those of F are known? We give a method based on explicit extension...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 1997
ISSN: 1071-5797
DOI: 10.1006/ffta.1997.0185