Zeta-functions of binary Hermitian forms and special values of Eisenstein series

DOI10.1007/BF01457865zbMath0659.10021OpenAlexW1998580304MaRDI QIDQ1112089

Jürgen Elstrodt, Jens Mennicke, Fritz J. Grunewald

Publication date: 1987

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

Full work available at URL: https://eudml.org/doc/164273

zbMATH Keywords

tablesEisenstein seriesHilbert symbolDirichlet seriesgenusperiodslocal densitiesrepresentation numbersrepresentations of numbersFourier coefficients of cusp forms of weight 2L-series of certain elliptic curvesspecial values of Eisenstein serieszeta-functions of binary Hermitian forms

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Analytic theory (Epstein zeta functions; relations with automorphic forms and functions) (11E45) Modular and automorphic functions (11F03) Special algebraic curves and curves of low genus (14H45) Theta series; Weil representation; theta correspondences (11F27) Special values of automorphic (L)-series, periods of automorphic forms, cohomology, modular symbols (11F67) Hurwitz and Lerch zeta functions (11M35) General binary quadratic forms (11E16)

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An explicit formula of the Koecher-Maass series associated with Hermitian modular forms belonging to the Maass space, Hilbert-Asai Eisenstein series, regularized products, and heat kernels, Zeta-functions of binary Hermitian forms, On two of Liouville's quaternary forms, Some remarks on discrete subgroups of \(SL_ 2({\mathbb{C}})\), Reflections in extended Bianchi groups, The trace of the heat kernel on a compact hyperbolic 3-orbifold, Vacuum energy for 3+1 dimensional space-time with compact hyperbolic spatial part, Eisenstein series whose Fourier coefficients are zeta functions of binary Hermitian forms, Large values of eigenfunctions on arithmetic hyperbolic 3-manifolds, Unitary periods, Hermitian forms and points on flag varieties, On the number of representations of integers by quaternary quadratic forms, Elliptic modular forms arising from zeta functions in two variables attached to the space of binary Hermitian forms, Koecher-Maass series associated to Hermitian modular forms of degree 2 and a characterization of cusp forms by the Hecke bound, A generalized Hermite constant for imaginary quadratic fields, From binary Hermitian forms to parabolic cocycles of Euclidean Bianchi groups

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