Towers of function fields with extremal properties
نویسنده
چکیده
For F/K an algebraic function field in one variable over a finite field of constants K (i.e., F is a finite algebraic extension of K(x) where x ∈ F is transcendental over K), let N(F ) and g(F ) denote the number of places of degree one and the genus, respectively, of F . Let F = (F1, F2, F3, . . .) be a tower of function fields, each defined over K. Further, we will assume that F1 ⊆ F2 ⊆ F3 . . ., where Fi+1/Fi is a finite separable extension and g(Fi) > 1 for some i ≥ 1. This follows the conventions of [7].
منابع مشابه
Galois Towers over Non-prime Finite Fields
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 ...
متن کاملTowers 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.
متن کاملOn the Invariants of Towers of Function Fields over Finite Fields
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...
متن کاملHyperinvariant subspaces and quasinilpotent operators
For a bounded linear operator on Hilbert space we define a sequence of the so-called weakly extremal vectors. We study the properties of weakly extremal vectors and show that the orthogonality equation is valid for weakly extremal vectors. Also we show that any quasinilpotent operator $T$ has an hypernoncyclic vector, and so $T$ has a nontrivial hyperinvariant subspace.
متن کاملExtremal shot noises, heavy tails and max-stable random fields
We consider the extremal shot noise defined by M(y) = sup{mh(y − x); (x,m) ∈ Φ}, where Φ is a Poisson point process on R × (0,+∞) with intensity λdxG(dm) and h : R → [0,+∞] is a measurable function. Extremal shot noises naturally appear in extreme value theory as a model for spatial extremes and serve as basic models for annual maxima of rainfall or for coverage field in telecommunications. In ...
متن کامل