Construction of eigenvarieties in small cohomological dimensions for semi-simple, simply connected groups.
Metaplectic covers of and the Gauss-Schering lemma
The Gauss-Schering Lemma is a classical formula for the Legendre symbol commonly used in elementary proofs of the quadratic reciprocity law. In this paper we show how the Gauss Schering Lemma may be generalized to give a formula for a -cocycle corresponding to a higher metaplectic extension of GL for any global field . In the case that has positive characteristic, our formula gives a complete construction of the metaplectic group and consequently an independent proof of the power reciprocity...
Dynamical zeta functions, congruences in Nielsen theory and Reidemeister torsion
In this paper we prove trace formulas for the Reidemeister numbers of group endomorphisms and the rationality of the Reidemeister zeta function in the following cases: the group is finitely generated and the endomorphism is eventually commutative; the group is finite; the group is a direct sum of a finite group and a finitely generated free Abelian group; the group is finitely generated, nilpotent and torsion free. We connect the Reidemeister zeta function of an endomorphism of a direct sum of a...
Metric diophantine approximation in Julia sets of expanding rational maps
The ergodic theory of shrinking targets.
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