On the existence and temperedness of cusp forms for SL3(Z)

DOI10.1515/crll.2001.029zbMath0996.11040arXivmath/0006058OpenAlexW2962692533MaRDI QIDQ2710297

Stephen D. Miller

Publication date: 24 April 2001

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0006058

zbMATH Keywords

Selberg trace formulacusp formWeyl lawtemperednessMass-Selberg relations

Mathematics Subject Classification ID

Other groups and their modular and automorphic forms (several variables) (11F55) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Spectral theory; trace formulas (e.g., that of Selberg) (11F72)

Related Items

The L² restriction norm of a GL₃ Maass form, Distribution of Hecke Eigenvalues for GL(n), Asymptotics of Automorphic Spectra and the Trace Formula, Optimal Diophantine exponents for \(\mathrm{SL}(n)\), Applications of the Kuznetsov formula on \(\mathrm{GL}(3)\), Weyl's law for the cuspidal spectrum of \(\mathrm{SL}_n\)., Sato-Tate equidistribution for families of Hecke-Maass forms on \(\mathrm{SL}(n,\mathbb{R})/\mathrm{SO}(n)\), Density results for automorphic forms on Hilbert modular groups II, A spectral mean value theorem for \(\text{GL}(3)\), Spectral asymptotics for arithmetic quotients of \(\text{SL}(n,{\mathbb R})/\text{SO}(n)\), The second moment of \(\mathrm{GL} (3) \times \mathrm{GL} (2)\) \(L\)-functions at special points from \(\mathrm{GL} (3)\) forms, A large sieve inequality of Elliott-Montgomery-Vaughan type for automorphic forms on \(\mathrm{GL}_3\), A method for computing general automorphic forms on general groups, Spectra of hyperbolic surfaces, Bounds for twists of \(\mathrm{GL}(3)\) \(L\)-functions, On the remainder term of the Weyl law for congruence subgroups of Chevalley groups, On the exceptional set of the generalized Ramanujan conjecture for \(\mathrm{GL}(3)\), EPSTEIN ZETA-FUNCTIONS, SUBCONVEXITY, AND THE PURITY CONJECTURE

Cites Work

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• Some properties of the Fourier transform on semi-simple Lie groups. I
• Weyl's law for \(SL(3,\mathbb{Z})\setminus SL(3,\mathbb{R})/SO(3,\mathbb{R})\)
• A relation between automorphic representations of ${\rm GL}(2)$ and ${\rm GL}(3)$