The density hypothesis for horizontal families of lattices

Mikołaj Frączyk, Gergely Harcos, Péter Maga, Djordje Milićević

Type: Article

Publication Date: 2024-01-18

Citations: 2

DOI: https://doi.org/10.1353/ajm.2024.a917540

Abstract

abstract: We prove the density hypothesis for wide families of arithmetic orbifolds arising from all division quaternion algebras over all number fields of bounded degree. Our power-saving bounds on the multiplicities of non-tempered representations are uniform in the volume and spectral aspects.

Locations

American Journal of Mathematics - View
Repository of the Academy's Library (Library of the Hungarian Academy of Sciences) - View - PDF
arXiv (Cornell University) - View - PDF

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Works Cited by This (51)

Action	Title	Year	Authors
+	Notes on the Generalized Ramanujan Conjectures	2005	Peter Sarnak
+	Statistical Properties of Eigenvalues of the Hecke Operators	1987	Peter Sarnak
+	Functoriality for the exterior square of 𝐺𝐿₄ and the symmetric fourth of 𝐺𝐿₂	2002	Henry Kim
+	Algebraic Number Theory	1999	Jürgen Neukirch
+	Sato-Tate equidistribution for families of Hecke-Maass forms on SL(n,R)/SO(n)	2015	Jasmin Matz Nicolas Templier
+	Groups and Geometric Analysis	2000	Sigurđur Helgason
+	Basic Number Theory	1967	André Weil
+ PDF Chat	Adeles and Algebraic Groups	1982	André Weil
+ PDF Chat	On a question of Lehmer and the number of irreducible factors of a polynomial	1979	Edward Dobrowolski
+ PDF Chat	Arithmetic of Hyperbolic Manifolds	1992	Colin M. MacLachlan Alan W. Reid