19,823 research outputs found
On the critical pair theory in abelian groups : Beyond Chowla's Theorem
We obtain critical pair theorems for subsets S and T of an abelian group such
that |S+T| < |S|+|T|+1. We generalize some results of Chowla, Vosper, Kemperman
and a more recent result due to Rodseth and one of the authors.Comment: Submitted to Combinatorica, 23 pages, revised versio
Densities of primes and realization of local extensions
In this paper we introduce new densities on the set of primes of a number
field. If is a Galois extension of number fields, we associate to any
element a density on primes of
. In particular, the density associated to is the usual Dirichlet
density on . After establishing some properties of these densities, we use
them to show that the maximal solvable extension of a number field unramified
outside an almost Chebotarev set realize the maximal local extension at each
prime lying outside this set.Comment: 19 pages; the main theorem appears now in a slightly generalized
version compared to v1. A section recalling stable sets is added. Several
small corrections are mad
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