Signature defects of cusps of Hilbert modular varieties and values of L- series at \(s=1\)

DOI10.4310/jdg/1214438992zbMath0575.10023OpenAlexW1486783616WikidataQ115187707 ScholiaQ115187707MaRDI QIDQ1064336

Werner Müller

Publication date: 1984

Published in: Journal of Differential Geometry (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4310/jdg/1214438992

zbMATH Keywords

Eisenstein seriesDolbeault operatorSelberg trace formuladimension formulaHilbert modular varietiesspectral resolutionHirzebruch conjectureindex of signaturesignature defects of cusp singularitiesvalues of L-series

Mathematics Subject Classification ID

Singularities of surfaces or higher-dimensional varieties (14J17) Index theory and related fixed-point theorems on manifolds (58J20) Representation-theoretic methods; automorphic representations over local and global fields (11F70) Automorphic forms on (mbox{GL}(2)); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces (11F41)

Related Items (15)

Index Theory and the Hypoelliptic Laplacian ⋮ Index theory of geometric Fredholm operators on varieties with isolated singularities ⋮ Transgressed Euler classes of ${\rm SL}(2n,\mathbf{Z})$ vector bundles, adiabatic limits of eta invariants and special values of $L$-functions ⋮ \(L^ 2\)-index theorems on locally symmetric spaces ⋮ Adiabatic Limits, Nonmultiplicativity of Signature, and Leray Spectral Sequence ⋮ The index theorem and the trace formula ⋮ On \(L^ 2\)-index theorems for complete manifolds of rank-one type ⋮ APS boundary conditions, eta invariants and adiabatic limits ⋮ The Atiyah–Singer index theorem ⋮ The duality of cusp singularities ⋮ Elliptic operators and higher signatures. ⋮ Théorie spectrale de quelques variétés à bouts ⋮ Transgressions of the Euler class and Eisenstein cohomology of \(\mathrm{GL}_N(\text{Z})\) ⋮ Analytic surgery and the eta invariant ⋮ The mathematical work of V. K. Patodi

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