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31.
We give a purely algebro-geometric proof of the fact that every nonsingular
projective curve can be defined over a finite extension of its moduli field.
This extends a result byWolfart [7] to curves over fields of arbitrary
characteristic.
Received: 30 November 2001 相似文献
32.
Miho Aoki 《Journal of Number Theory》2003,101(2):270-293
In this paper, we will determine the structure of a certain module which is related to the plus part of the ideal class groups in terms of the divisibility of Gauss sums in some local fields. This result is a generalization of a result of Iwasawa and the previous work of Ichimura and Hachimori. 相似文献
33.
This paper deals with the inversive congruential method with power of two modulusm for generating uniform pseudorandom numbers. Statistical independence properties of the generated sequences are studied based on the distribution of triples of successive pseudorandom numbers. It is shown that there exist parameters in the inversive congruential method such that the discrepancy of the corresponding point sets in the unit cube is of an order of magnitude at leastm
–1/3. The method of proof relies on a detailed analysis of certain rational exponential sums. 相似文献
34.
35.
Wolfgang M. Ruppert 《manuscripta mathematica》1998,96(1):17-22
If K is a number field of degree n over Q with discriminant D
K
and if α∈K generates K, i.e. K=Q(α), then the height of α satisfies with . The paper deals with the existence of small generators of number fields in this sense. We show: (1) For each $n$ there are
infinitely many number fields K of degree $n$ with a generator α such that . (2) There is a constant d
2 such that every imaginary quadratic number field has a generator α which satisfies .?(3) If K is a totally real
number field of prime degree n then one can find an integral generator α with .
Received: 10 January 1997 / Revised version: 13 January 1998 相似文献
36.
In 1957 Robert Ellis proved that a group with a locally compact Hausdorff topology T making all translations continuous also has jointly continuous multiplication and continuous inversion, and is thus a topological group. The theorem does not apply to locally compact asymmetric spaces such as the reals with addition and the topology of upper open rays. We first show a bitopological Ellis theorem, and then introduce a generalization of locally compact Hausdorff, called locally skew compact, and a topological dual, Tk, to obtain the following asymmetric Ellis theorem which applies to the example above:Whenever (X,⋅,T) is a group with a locally skew compact topology making all translations continuous, then multiplication is jointly continuous in both (X,⋅,T) and (X,⋅,Tk), and inversion is a homeomorphism between (X,T) and (X,Tk).This generalizes the classical Ellis theorem, because T=Tk when (X,T) is locally compact Hausdorff. 相似文献
37.
We show that the existence of a non-metrizable compact subspace of a topological group G often implies that G contains an uncountable supersequence (a copy of the one-point compactification of an uncountable discrete space). The existence of uncountable supersequences in a topological group has a strong impact on bounded subsets of the group. For example, if a topological group G contains an uncountable supersequence and K is a closed bounded subset of G which does not contain uncountable supersequences, then any subset A of K is bounded in G?(K?A). We also show that every precompact Abelian topological group H can be embedded as a closed subgroup into a precompact Abelian topological group G such that H is bounded in G and all bounded subsets of the quotient group G/H are finite. This complements Ursul's result on closed embeddings of precompact groups to pseudocompact groups. 相似文献
38.
39.
Sergio Albeverio Volodymyr Koshmanenko Mykola Pratsiovytyi Grygoriy Torbin 《Positivity》2006,10(1):39-49
We introduce the conflict interaction with two positions between a couple of image probability measures and consider the associated
dynamical system. We prove the existence of invariant limiting measures and find the criteria for these measures to be a pure
point, absolutely continuous, or singular cotinuous as well as to have any topological type and arbitary Hausdorff dimension. 相似文献
40.