Cusp forms and eigenfunctions of the Laplacian

DOI10.1007/BF01451932zbMath0439.30031OpenAlexW2004466230MaRDI QIDQ1142330

Anton Good

Publication date: 1981

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

Full work available at URL: https://eudml.org/doc/182858

zbMATH Keywords

Eisenstein seriesFuchsian groupeigenfunctions of the Laplacian

Mathematics Subject Classification ID

Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization) (30F35)

Related Items (23)

Dirichlet and Poincaré series ⋮ Bounds on shifted convolution sums for Hecke eigenforms ⋮ On shifted convolutions of \(\zeta^3(s)\) with automorphic \(L\)-functions ⋮ Oscillations of Hecke eigenvalues at shifted primes ⋮ SPECIAL VALUES OF SHIFTED CONVOLUTION DIRICHLET SERIES ⋮ Subconvexity bounds for Rankin-Selberg \(L\)-functions for congruence subgroups ⋮ Sparse equidistribution problems, period bounds and subconvexity ⋮ Subconvexity bounds for triple \(L\)-functions and representation theory ⋮ Multiple Dirichlet series and shifted convolutions ⋮ Sums of \(k\)-th powers and Fourier coefficients of cusp forms ⋮ Triple correlation sums of coefficients of cuspidal forms ⋮ The Bombieri–Vinogradov Theorem on Higher Rank Groups and its Applications ⋮ The spectral decomposition of shifted convolution sums ⋮ The spectral decomposition of shifted convolution sums over number fields ⋮ Remark on the paper ``On products of Fourier coefficients of cusp forms ⋮ Real zeros and size of Rankin-Selberg \(L\)-functions in the level aspect ⋮ Rankin-Selberg without unfolding and bounds for spherical Fourier coefficients of Maass forms ⋮ Small gaps in coefficients of \(L\)-functions and \({\mathfrak B}\)-free numbers in short intervals ⋮ Effective equidistribution of twisted horocycle flows and horocycle maps ⋮ On exponential sums for coefficients of general L-functions ⋮ Renormalization of integrals of products of Eisenstein series and analytic continuation of representations ⋮ On the Topography of Maass Waveforms for PSL(2, Z) ⋮ Bounding hyperbolic and spherical coefficients of Maass forms

Cites Work

• Local analysis of Selberg's trace formula
• Beiträge zur Theorie der Dirichletreihen, die Spitzenformen zugeordnet sind
• Das Eigenwertproblem der automorphen Formen in der hyperbolischen Ebene. I, II. (The eigenvalue problem of automorphic forms in the hyperbolic plane. I. II)
• Über eine Metrisierung der automorphen Formen und die Theorie der Poincaréschen Reihen
• Discontinuous groups
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