Convolution Dirichlet Series and a Kronecker Limit Formula for Second-Order Eisenstein Series

DOI10.1017/S0027763000025605zbMath1098.11028arXivmath/0404002MaRDI QIDQ3374117

Cormac O'Sullivan, Jay A. Jorgenson

Publication date: 9 March 2006

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0404002

zbMATH Keywords

modular formEisenstein seriesFuchsian groupCusp formKronecker limit

Mathematics Subject Classification ID

Forms of half-integer weight; nonholomorphic modular forms (11F37) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Fourier coefficients of automorphic forms (11F30)

Related Items (12)

Generalized Dedekind sums and equidistribution mod 1 ⋮ Modular Dedekind symbols associated to Fuchsian groups and higher-order Eisenstein series ⋮ The Manin-Drinfeld theorem and the rationality of Rademacher symbols ⋮ Extended higher Herglotz functions. I: Functional equations ⋮ The dimensions of spaces of holomorphic second-order automorphic forms and their cohomology ⋮ Transformation laws for generalized Dedekind sums associated to Fuchsian groups ⋮ Bounds for canonical Green's function at cusps ⋮ Kernels of \(L\)-functions of cusp forms ⋮ Unipotent vector bundles and higher-order non-holomorphic Eisenstein series ⋮ Dedekind sums, reciprocity, and non-arithmetic groups ⋮ Some results in study of Kronecker limit formula and Dedekind sums ⋮ Bounds for Green's functions on noncompact hyperbolic Riemann orbisurfaces of finite volume

Cites Work

• Crossing probabilities and modular forms
• Estimating additive character sums for Fuchsian groups
• The cubic moment of central values of automorphic \(L\)-functions
• Modular symbols have a normal distribution
• A Kronecker limit formula for real quadratic fields
• Continued fractions, modular symbols, and noncommutative geometry
• Analytic torsion for complex manifolds
• Values of the Dedekind Eta Function at Quadratic Irrationalities
• Hilbert-Asai Eisenstein series, regularized products, and heat kernels
• Second order modular forms
• Properties of Eisenstein series formed with modular symbols
• On a Certain Function Analogous to log|η(z)|
• Dedekind Sums for a Fuchsian Group, I
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