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We prove an upper bound for the number of shortest closed geodesics in a closed hyperbolic manifold of any dimension in terms of its volume and systole, generalizing a theorem of Parlier for surfaces.
Harmonic analysis and discontinuous groups in weakly symmetric Riemannian spaces with applications to Dirichlet series
A. Selberg · 1956
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Zur analytischen Theorie hyperbolischen Raumformen und Bewegungsgruppen
H. Huber · 1959
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A proof of Selberg’s hypothesis
D.A. Každan and G.A. Margulis · 1968
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Topics on totally discontinuous groups
H.C. Wang · 1972
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Collars on Riemann surfaces
L. Keen · 1974
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Riemannsche Flächen mit Eigenwerten in ( 0 CLOSE , (0, OPEN 1 / 4 ) 1/4)
P. Buser · 1977
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Length spectrum for compact locally symmetric spaces of strictly negative curvature
D.L. DeGeorge · 1977
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The length spectra of some compact manifolds of negative curvature
R. Gangolli · 1977
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On bounds for packings on the sphere and in space
G.A. Kabatyanskiĭ and V.I. Levenshteĭn · 1978
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On Cheeger’s inequality λ 1 ≥ h 2 / 4 \lambda_{1}\geq h^{2}/4
P. Buser · 1980
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The Selberg trace formula
B. Randol · 1984
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The Selberg trace formula and the Ruelle zeta function for compact hyperbolics
A. Deitmar · 1989
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Lectures on hyperbolic geometry
R. Benedetti and C. Petronio · 1992
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Geometry and spectra of compact Riemann surfaces
P. Buser · 1992
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The Selberg trace formula and the Selberg zeta function for cocompact discrete subgroups of SO + ( 1 , n ) {\rm SO}_{+}(1,n)
L.B. Parnovskiĭ · 1992
Cited alongside, same era.
Tubes and eigenvalues for negatively curved manifolds
P. Buser, B. Colbois, and J. Dodziuk · 1993
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Fourier analysis
E.M. Stein and R. Shakarchi · 2003
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Kissing numbers, sphere packings, and some unexpected proofs
F. Pfender and G.M. Ziegler · 2004
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Pour toute surface hyperbolique de genre g , λ 2 g − 2 > 1 / 4 g,\ \lambda_{2g-2}>1/4
J.-P. Otal and E. Rosas · 2009
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Kissing numbers for surfaces
H. Parlier · 2013
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Systoles and kissing numbers of finite area hyperbolic surfaces
F. Fanoni and H. Parlier · 2015
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Packing curves on surfaces with few intersections
T. Aougab, I. Biringer, and J. Gaster · 2017
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Systoles on Riemann surfaces
P. Schmutz · 1994
Cited alongside, same era.
Extremal Riemann surfaces with a large number of systoles
P. Schmutz Schaller · 1997
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Sphere packings, lattices and groups
J.H. Conway and N.J.A. Sloane · 1999
Cited alongside, same era.
New upper bounds on sphere packings. I
H. Cohn and N. Elkies · 2003
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H. Cohn, A. Kumar, S.D. Miller, D. Radchenko, and M. Viazovska · 2017
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The sphere packing problem in dimension 8
M.S. Viazovska · 2017
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Lattices with exponentially large kissing numbers
S. Vlăduţ · 2018
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