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Lecture Notes in Mathematics
cover

Local Newforms for GSp(4)

Authors: Brooks, Roberts, Schmidt, Ralf

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About this book

Local Newforms for GSp(4) describes a theory of new- and oldforms for representations of GSp(4) over a non-archimedean local field. This theory considers vectors fixed by the paramodular groups, and singles out certain vectors that encode canonical information, such as L-factors and epsilon-factors, through their Hecke and Atkin-Lehner eigenvalues. While there are analogies to the GL(2) case, this theory is novel and unanticipated by the existing framework of conjectures. An appendix includes extensive tables about the results and the representation theory of GSp(4).

Reviews

From the reviews:

"This book gives an analog of Casselman’s local Atkin-Lehner theorem for GSp(4). … The local theory of the Novodvorsky construction is advanced by this work of Roberts and Schmidt, and the converse is also true: the Novodvorsky local integrals play an important role in the proof, especially in the supercuspidal case. … proves an important theorem, and moreover is written in a useful and instructive way." (Daniel Bump, Mathematical Reviews, Issue 2008 g)


Table of contents (7 chapters)

Table of contents (7 chapters)
  • A Summary

    Pages 1-25

  • Representation Theory

    Pages 27-83

  • Paramodular Vectors

    Pages 85-122

  • Zeta Integrals

    Pages 123-149

  • Non-supercuspidal Representations

    Pages 151-186

Buy this book

eBook $59.99
price for USA in USD (gross)
  • ISBN 978-3-540-73324-9
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $74.99
price for USA in USD
  • ISBN 978-3-540-73323-2
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Local Newforms for GSp(4)
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
1918
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-73324-9
DOI
10.1007/978-3-540-73324-9
Softcover ISBN
978-3-540-73323-2
Series ISSN
0075-8434
Edition Number
1
Number of Pages
VIII, 312
Topics