Local Newforms for GSp(4)

Buch | Softcover
VIII, 312 Seiten
2007 | 2007
Springer Berlin (Verlag)
978-3-540-73323-2 (ISBN)

Lese- und Medienproben

Local Newforms for GSp(4) - Brooks Roberts, Ralf Schmidt
53,49 inkl. MwSt

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).

A Summary.- Representation Theory.- Paramodular Vectors.- Zeta Integrals.- Non-supercuspidal Representations.- Hecke Operators.- Proofs of the Main Theorems.

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)

Erscheint lt. Verlag 20.8.2007
Reihe/Serie Lecture Notes in Mathematics
Zusatzinfo VIII, 312 p.
Verlagsort Berlin
Sprache englisch
Maße 155 x 235 mm
Gewicht 488 g
Themenwelt Mathematik / Informatik Mathematik Algebra
Mathematik / Informatik Mathematik Arithmetik / Zahlentheorie
Mathematik / Informatik Mathematik Wahrscheinlichkeit / Kombinatorik
Schlagworte algebraic number theory • eigenvalue • MSC(2000): 11F46, 11F70, 22E50 • Newforms • Node • oldforms • paramodular • representations • Representation Theory • Siegel • Zahlentheorie
ISBN-10 3-540-73323-X / 354073323X
ISBN-13 978-3-540-73323-2 / 9783540733232
Zustand Neuware
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