On the representation of integers by the Lorentzian quadratic form

DOI10.1006/jfan.1997.3129zbMath0883.11017OpenAlexW1993127716MaRDI QIDQ1376564

John G. Ratcliffe, Steven T. Tschantz

Publication date: 23 March 1998

Published in: Journal of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jfan.1997.3129

zbMATH Keywords

sums of squaresquadratic formasymptotic formulalocal densitieslattice pointnumber of representations of an integer

Mathematics Subject Classification ID

Sums of squares and representations by other particular quadratic forms (11E25) Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45)

Related Items (4)

Apollonian circle packings: Number theory ⋮ Apollonian circle packings: number theory. II: Spherical and hyperbolic packings ⋮ A numerical study on exceptional eigenvalues of certain congruence subgroups of \(\mathrm {SO}(n,1)\) and \(\mathrm {SU}(n,1)\) ⋮ An asymptotic formula for representations of integers by indefinite hermitian forms

Cites Work

• Über die Verteilung der Längen geodätischer Lote in hyperbolischen Raumformen
• The asymptotic distribution of lattice points in Euclidean and non-Euclidean spaces
• Kloosterman sums for Clifford algebras and a lower bound for the positive eigenvalues of the Laplacian for congruence subgroups acting on hyperbolic spaces
• Poincaré series for \(SO(n,1)\)
• Density of integer points on affine homogeneous varieties
• Mixing, counting, and equidistribution in Lie groups
• The circle problem in the hyperbolic plane
• Hardy-Littlewood varieties and semisimple groups
• Lectures on quadratic forms. Reissued
• Über die analytische Theorie der quadratischen Formen. II
• The Divisors of a Quadratic Polynomial
• Asymptotic formulae for the number of lattice points in Euclidean and Lobachevskii spaces
• Arithmetic Applications of the Hyperbolic Lattice Point Theorem
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