Displaying similar documents to “L-functions at the origin and annihilation of class groups in multiquadratic extensions”

On the S-Euclidean minimum of an ideal class

Kevin J. McGown (2015)

Acta Arithmetica

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We show that the S-Euclidean minimum of an ideal class is a rational number, generalizing a result of Cerri. In the proof, we actually obtain a slight refinement of this and give some corollaries which explain the relationship of our results with Lenstra's notion of a norm-Euclidean ideal class and the conjecture of Barnes and Swinnerton-Dyer on quadratic forms. In particular, we resolve a conjecture of Lenstra except when the S-units have rank one. The proof is self-contained but uses...

Remarks on Yu’s ‘property A’ for discrete metric spaces and groups

Jean-Louis Tu (2001)

Bulletin de la Société Mathématique de France

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Guoliang Yu has introduced a property on discrete metric spaces and groups, which is a weak form of amenability and which has important applications to the Novikov conjecture and the coarse Baum–Connes conjecture. The aim of the present paper is to prove that property in particular examples, like spaces with subexponential growth, amalgamated free products of discrete groups having property A and HNN extensions of discrete groups having property A.

The Ore conjecture

Martin Liebeck, E.A. O’Brien, Aner Shalev, Pham Tiep (2010)

Journal of the European Mathematical Society

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The Ore conjecture, posed in 1951, states that every element of every finite non-abelian simple group is a commutator. Despite considerable effort, it remains open for various infinite families of simple groups. In this paper we develop new strategies, combining character-theoretic methods with other ingredients, and use them to establish the conjecture.

On Brauer’s Height Zero Conjecture

Gabriel Navarro, Britta Späth (2014)

Journal of the European Mathematical Society

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In this paper, the unproven half of Richard Brauer’s Height Zero Conjecture is reduced to a question on simple groups.

The Bass conjecture and growth in groups

Anders Karlsson, Markus Neuhauser (2004)

Colloquium Mathematicae

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We discuss Bass's conjecture on the vanishing of the Hattori-Stallings rank from the viewpoint of geometric group theory. It is noted that groups without u-elements satisfy this conjecture. This leads in particular to a simple proof of the conjecture in the case of groups of subexponential growth.