منابع مشابه
Number 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 کاملSmall 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 کاملA note on generators of number fields
We establish upper bounds for the smallest height of a generator of a number field k over the rational field Q. Our first bound applies to all number fields k having at least one real embedding. We also give a second conditional result for all number fields k such that the Dedekind zeta-function associated to the Galois closure of k/Q satisfies GRH. This provides a partial answer to a question ...
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 کاملPeriod Distribution of Inversive Pseudorandom Number Generators Over Finite Fields
In this paper, we focus on analyzing the period distribution of the inversive pseudorandom number generators (IPRNGs) over finite field (ZN ,+,×), where N > 3 is a prime. The sequences generated by the IPRNGs are transformed to 2-dimensional linear feedback shift register (LFSR) sequences. By employing the generating function method and the finite field theory, the period distribution is obtain...
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ژورنال
عنوان ژورنال: manuscripta mathematica
سال: 1998
ISSN: 0025-2611,1432-1785
DOI: 10.1007/s002290050051