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We show that, for random walks on Cayley graphs, the long time behavior of the probability of
return after 2n steps is invariant by quasi-isometry.
One interesting application of Theorem 0.1 is given in [DG, x3], where it is used to analyze the niteness
of the number of solutions to certain generalized Fermat equations. Another application of T...
Generalized word type pattern for nonregular factorial designs with multiple groups of factors
type pattern Generalized word
2015/3/18
Consideran(sr )sn factorialdesignD= [D0,DT]inst runs,involvingone
sr -levelfactor (r≥2),groupedbytheLrs-levelfactors,andns-level
factors.
A note on Freiman models in Heisenberg groups
Freiman models Heisenberg groups Number Theory
2012/7/11
Green and Ruzsa recently proved that for any $s\ge2$, any small squaring set $A$ in a (multiplicative) abelian group, i.e. $|A\cdot A|s a Freiman $s$-model: it means that there exists a grou...
The local-global exact sequence for Chow groups of zero-cycles
zero-cycles local-global principle Brauer–Manin obstruction
2012/6/27
A local-global sequence for Chow groups of zero-cycles involving Brauer groups has been conjectured to be exact for all proper smooth algebraic varieties. We apply existing methods to construct severa...
Residual automorphic forms and spherical unitary representations of exceptional groups
Arthur’s conjectures unitary dual residual Eisenstein series automorphic realizations
2012/5/25
Arthur has conjectured that the unitarity of a number of representations can be shown by finding appropriate automorphic realizations. This has been verified for classical groups by Moeglin and for th...
On the Dimension of Cohomology of Bianchi Groups
Dimension Cohomology Bianchi Groups Number Theory
2012/4/18
Using Lefschetz numbers of certain involutions, we provide lower bounds for the cuspidal cohomology of principal congruence subgroups of Bianchi groups. The asymptotic lower bounds that follow from ou...
Deforming endomorphisms of supersingular Barsotti-Tate groups
Deforming endomorphisms supersingular Barsotti-Tate groups Number Theory
2012/3/1
The formal deformation space of a supersingular Barsotti-Tate group over of dimension two equipped with an action of Z_{p^2} is known to be isomorphic to the formal spectrum of a power series ring in ...
The Geometrical Satake Correspondence for Ramified Groups
Geometrical Satake Correspondence Ramified Groups Number Theory
2011/9/22
Abstract: We prove the geometrical Satake isomorphism for a reductive group defined over F=k((t)), and split over a tamely ramified extension. As an application, we give a description of the nearby cy...
On Truncation of irreducible representations of Chevalley groups
irreducible representations Chevalley groups Number Theory
2011/9/14
Abstract: We prove part of a higher rank analogue of the Mazur-Gouvea Conjecture. More precisely, let $\tilde{\bf G}$ be a connected, reductive ${\Bbb Q}$-split group and let $\Gamma$ be an arithmetic...
Enhanced Gauge Groups in N=4 Topological Amplitudes and Lorentzian Borcherds Algebras
Gauge Groups Topological Amplitudes Lorentzian Borcherds Algebras
2011/9/30
Abstract: We continue our study of algebraic properties of N=4 topological amplitudes in heterotic string theory compactified on T^2, initiated in arXiv:1102.1821. In this work we evaluate a particula...
Non-abelian $p$-adic $L$-functions and Eisenstein series of unitary groups; the CM method
Eisenstein series unitary groups the CM method Number Theory
2011/8/26
Abstract: In this work we prove the so-called "torsion congruences" between abelian $p$-adic $L$-functions that are related to automorphic representations of definite unitary groups. These congruences...
Diophantine Geometry over Groups X: The Elementary Theory of Free Products of Groups
Diophantine Geometry Groups X Elementary Theory of Free Products of Groups
2011/1/14
This paper is the 10th in a sequence on the structure of sets of solutions to systems of equations over groups, projections of such sets (Diophantine sets), and the structure of definable sets over fe...
On Extending the Langlands-Shahidi Method to Arithmetic Quotients of Loop Groups
automorphic L-functions Eisenstein series loop groups
2010/12/10
We discuss certain Eisenstein series on arithmetic quotients of loop groups, ˆG , which are associated to cusp forms on finite-dimensional groups associated with maximal parabolics of ˆG .
Almost regular involutory automorphisms of uniquely 2-divisible groups
almost regular involutory automorphism uniquely 2-divisible group
2010/11/29
We prove that a uniquely 2-divisible group that admits an almost regular involutory automorphism is solvable.