منابع مشابه
The Artin conjecture for some S5-extensions
We establish some new cases of Artin’s conjecture. Our results apply to Galois representations over Q with image S5 satisfying certain local hypotheses, the most important of which is that complex conjugation is conjugate to (12)(34). In fact, we prove the stronger claim conjectured by Langlands that these representations are automorphic. For the irreducible representations of dimensions 4 and ...
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The Illumination Conjecture was raised independently by Boltyanski and Hadwiger in 1960. According to this conjecture any d-dimensional convex body can be illuminated by at most 2d light sources. This is an important fundamental problem. The paper surveys the state of the art of the Illumination Conjecture. 1 1 The Illumination Conjecture Let K be a convex body (i.e. a compact convex set with n...
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The Atiyah conjecture for a discrete group G states that the L-Betti numbers of a finite CW-complex with fundamental group G are integers if G is torsion-free, and in general that they are rational numbers with denominators determined by the finite subgroups of G. Here we establish conditions under which the Atiyah conjecture for a torsion-free group G implies the Atiyah conjecture for every fi...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2003
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa108-4-5