On a construction of certain classes of cuspidal automorphic forms via Poincaré series

DOI10.1007/s00208-008-0269-5zbMath1185.11037OpenAlexW2040820959MaRDI QIDQ957896

Goran Muić

Publication date: 1 December 2008

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00208-008-0269-5

zbMATH Keywords

Poincaré seriescuspidal automorphic forms

Mathematics Subject Classification ID

Representation-theoretic methods; automorphic representations over local and global fields (11F70) Representations of Lie and linear algebraic groups over global fields and adèle rings (22E55)

Related Items (16)

Fourier coefficients of automorphic forms and integrable discrete series ⋮ On the non-vanishing of \(L\)-functions associated to cusp forms of half-integral weight ⋮ On holomorphic projection for symplectic groups ⋮ Non-vanishing of vector-valued Poincaré series ⋮ On a family of Siegel Poincaré series ⋮ On the Schwartz space \(\mathcal{S}(G(k) \backslash G(\mathbb{A}))\) ⋮ Modular curves and bases for the spaces of cuspidal modular forms ⋮ ON THE NON-VANISHING OF CERTAIN MODULAR FORMS ⋮ On existence of generic cusp forms on semisimple algebraic groups ⋮ Spectral decomposition of compactly supported Poincaré series and existence of cusp forms ⋮ On the non-vanishing of Poincaré series on the metaplectic group ⋮ On geometric density of Hecke eigenvalues for certain cusp forms ⋮ On the structure of the space of cusp forms for a semisimple group over a number field ⋮ On the cusp forms for the congruence subgroups of \(\text{SL}_{2}(\mathbb R)\) ⋮ On the cuspidal modular forms for the Fuchsian groups of the first kind ⋮ Smooth cuspidal automorphic forms and integrable discrete series

Cites Work

• Poincaré series for \(SO(n,1)\)
• Asymptotic behaviour of matrix coefficients of the discrete series
• Cusp forms
• A proof of Langlands' conjecture on Plancherel measures; complementary series for \(p\)-adic groups
• Some finiteness properties of adele groups over number fields
• Compactification of arithmetic quotients of bounded symmetric domains
• Discrete series for semisimple Lie groups. II: Explicit determination of the characters
• On the cuspidal cohomology of arithmetic groups
• Automorphic Forms and L-Functions for the GroupGL(n, R)
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