منابع مشابه
Small generators of function fields
Let K/k be a finite extension of a global field. Such an extension can be generated over k by a single element. The aim of this article is to prove the existence of a ”small” generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.
متن کاملSmall generators of function fields par
Let K/k be a finite extension of a global field. Such an extension can be generated over k by a single element. The aim of this article is to prove the existence of a ”small“ generator in the function field case. This answers the function field version of a question of Ruppert on small generators of number fields.
متن کاملNumber Fields without Small Generators
Let D > 1 be an integer, and let b = b(D) > 1 be its smallest divisor. We show that there are infinitely many number fields of degree D whose primitive elements all have relatively large height in terms of b, D and the discriminant of the number field. This provides a negative answer to a questions of W. Ruppert from 1998 in the case when D is composite. Conditional on a very weak form of a fol...
متن کاملOn Generators of Arithmetic Groups over Function Fields
Fq = the finite field with q elements; throughout the paper q is assumed to be odd. A = Fq[T ], T indeterminate. F = Fq(T ) = the fraction field of A. |F | = the set of places of F . For x ∈ |F |, Fx = the completion of F at x. Ox = {z ∈ Fx | ordx(z) ≥ 0} = the ring of integers of Fx. Fx = the residue field of Ox; deg(x) = [Fx : Fq]. For 0 = f ∈ A, deg(f) = the degree of f as a polynomial in T ...
متن کاملGenerators of Finite Fields with Powers of Trace Zero and Cyclotomic Function Fields
Using the relation between the problem of counting irreducible polynomials over finite fields with some prescribed coefficients to the problem of counting rational points on curves over finite fields whose function fields are subfields of cyclotomic function fields, we count the number of generators of finite fields with powers of trace zero up to some point, answering a question of Z. Reichste...
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ژورنال
عنوان ژورنال: Journal de Théorie des Nombres de Bordeaux
سال: 2010
ISSN: 1246-7405
DOI: 10.5802/jtnb.744