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When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is so, and conjecture precise conditions.
Reading the bibliography…
When does the amount of torsion in the homology of an arithmetic group grow exponentially with the covolume? We give many examples where this is so, and conjecture precise conditions.
Reading the bibliography…
Transcendental and algebraic numbers
A. O. Gel ′ · 1960
Earlier work this paper cites.
A duality theorem for Reidemeister torsion
John Milnor · 1962
Earlier work this paper cites.
Complex powers of an elliptic operator
R. T. Seeley · 1967
Earlier work this paper cites.
Harmonic analysis on real reductive groups. I. The theory of the constant term
Harish-Chandra · 1975
Earlier work this paper cites.
A proof of Blattner’s conjecture
Henryk Hecht and Wilfried Schmid · 1975
Earlier work this paper cites.
Harmonic analysis on real reductive groups. III. The Maass-Selberg relations and the Plancherel formula
Harish-Chandra · 1976
Earlier work this paper cites.
Analytic torsion and R R -torsion of Riemannian manifolds
Werner Müller · 1978
Earlier work this paper cites.
Analytic torsion and the heat equation
Jeff Cheeger · 1979
Earlier work this paper cites.
The volume of a compact Lie group
I. G. Macdonald · 1980
Earlier work this paper cites.
Criteria for the unitarizability of some highest weight modules
R. Parthasarathy · 1980
Earlier work this paper cites.
Criteria for the unitarizability of some highest weight modules
R. Parthasarathy · 1980
Earlier work this paper cites.
On the upper estimate of the heat kernel of a complete Riemannian manifold
Siu Yuen Cheng, Peter Li, and Shing Tung Yau · 1981
Earlier work this paper cites.
PSL ( 2 ) {\rm PSL}(2) over imaginary quadratic integers
J. Elstrodt, F. Grunewald, and J. Mennicke · 1982
Earlier work this paper cites.
Dynamical properties of quasihyperbolic toral automorphisms
D. A. Lind · 1982
Earlier work this paper cites.
L 2 L^{2} -index and the Selberg trace formula
Dan Barbasch and Henri Moscovici · 1983
Earlier work this paper cites.
Heuristics on class groups of number fields
H. Cohen and HW Lenstra Jr · 1983
Earlier work this paper cites.
Unitary representations with nonzero cohomology
David A. Vogan, Jr. and Gregg J. Zuckerman · 1984
Cited alongside, same era.
Representation theory of semisimple groups
Anthony W. Knapp · 1986
Cited alongside, same era.
Real reductive groups. I
Nolan R. Wallach · 1988
Cited alongside, same era.
Lie groups and Lie algebras. Chapters 1–3
Nicolas Bourbaki · 1989
Cited alongside, same era.
Heat kernels on covering spaces and topological invariants
John Lott · 1992
Cited alongside, same era.
Arithmetic quantum chaos
Peter Sarnak · 1992
Cited alongside, same era.
Groups and expanders
A. Lubotzky and B. Weiss · 1993
Cited alongside, same era.
Analytic torsion and R R -torsion for unimodular representations
Werner Müller · 1993
Cited alongside, same era.
Approximating L 2 L^{2} -invariants by their finite-dimensional analogues
W. Lück · 1994
Cited alongside, same era.
Cohomologie galoisienne
Jean-Pierre Serre · 1994
Cited alongside, same era.
On the cuspidal cohomology of S S -arithmetic subgroups of reductive groups over number fields
A. Borel, J.-P. Labesse, and J. Schwermer · 1996
Cited alongside, same era.
Heights of polynomials and entropy in algebraic dynamics
Graham Everest and Thomas Ward · 1999
Cited alongside, same era.
L 2 L^{2} -invariants: theory and applications to geometry and K K -theory
Wolfgang Lück · 2002
Later among the works it cites.
L 2 L^{2} -invariants of locally symmetric spaces
Martin Olbrich · 2002
Later among the works it cites.
Mahler measure, links and homology growth
Daniel S. Silver and Susan G. Williams · 2002
Later among the works it cites.
Torsion numbers of augmented groups with applications to knots and links
Daniel S. Silver and Susan G. Williams · 2002
Later among the works it cites.
Growth of Betti numbers
Bryan Clair and Kevin Whyte · 2003
Later among the works it cites.
Automorphic forms and rational homology 3-spheres
Frank Calegari and Nathan M. Dunfield · 2006
Later among the works it cites.
Finite covers of random 3-manifolds
Nathan M. Dunfield and William P. Thurston · 2006
Later among the works it cites.
On the interpolation of systems of eigenvalues attached to automorphic Hecke eigenforms
Matthew Emerton · 2006
Later among the works it cites.
An L 2 L^{2} -Alexander invariant for knots
Weiping Li and Weiping Zhang · 2006
Later among the works it cites.
Mass formulae for extensions of local fields, and conjectures on the density of number field discriminants
Manjul Bhargava · 2007
Later among the works it cites.
Criteria for virtual fibering
Ian Agol · 2008
Later among the works it cites.
Cohomological goodness and the profinite completion of Bianchi groups
F. Grunewald, A. Jaikin-Zapirain, and P. A. Zalesskii · 2008
Later among the works it cites.
Cohomology of number fields
Jürgen Neukirch, Alexander Schmidt, and Kay Wingberg · 2008
Later among the works it cites.
Nearly ordinary Galois deformations over arbitrary number fields
Frank Calegari and Barry Mazur · 2009
Later among the works it cites.
On Ihara’s lemma for Hilbert modular varieties
Mladen Dimitrov · 2009
Later among the works it cites.
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