Introduction to Automorphic Representations

With a view toward trace formulae

Inbunden, Engelska, 2024

Av Jayce R. Getz, Heekyoung Hahn

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Thus supercuspidal representations are defined locally, cuspidal representations and Eisenstein series are defined globally, and Rankin-Selberg L-functions are defined to give a link between the global and local settings.

Produktinformation

Utgivningsdatum2024-03-02
Mått152 x 228 x 20 mm
Vikt1 158 g
FormatInbunden
SpråkEngelska
SerieGraduate Texts in Mathematics
Antal sidor609
FörlagSpringer International Publishing AG
ISBN9783031411519

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Jayce R. Getz is Associate Professor of Mathematics at Duke University. His research in number theory spans several subjects --- algebraic geometry, automorphic representations, harmonic analysis, and trace formulae. His monograph with M. Goresky (Institute for Advanced Studies), Hilbert Modular Forms with Coefficients in Intersection Homology and Quadratic Base Change, was awarded the 2011 Ferran Sunyer i Balaguer Prize.Heekyoung Hahn is Associate Research Professor of Mathematics at Duke University. Her research covers additive combinatorics, Langlands functoriality, and related issues in the representation theory of algebraic groups.

1. Affine Algebraic Groups.- 2. Adeles.- 3. Discrete Automorphic Representations.- 4. Archimedean Representation Theory.- 5. Representations of Totally Disconnected Groups.- 6. Automorphic Forms.- 7. Unramified Representations.- 8. Nonarchimedean Representation Theory.- 9. The Cuspidal Spectrum.- 10. Einsenstein Series.- 11. Rankin-Selberg L-functions.- 12. Langlands Functoriality.- 13. Known Cases of Global Langlands Functoriality.- 14. Distinction and Period Integrals.- 15. The Cohomology of Locally Symmetric Spaces.- 16. Spectral Sides of the Trace Formulae.- 17. Orbital Integrals.- 18. Simple Trace Formulae.- 19. Applications of Trace Formulae.- A. Groups attached to involutions of algebras.- B. The Iwasawa Decomposition.- C. Poisson Summation.- D. Alternate conventions related to adelic quotients.- Hints to selected exercises.- References.- Index.