© 2007

Local Newforms for GSp(4)


Part of the Lecture Notes in Mathematics book series (LNM, volume 1918)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Pages 1-25
  3. Pages 27-83
  4. Pages 85-122
  5. Pages 123-149
  6. Pages 187-237
  7. Back Matter
    Pages 269-307

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).


Eigenvalue Newforms Node Representation theory Siegel algebraic number theory oldforms paramodular representations

Authors and affiliations

  1. 1.University of Idaho83844-1103MoscowUSA
  2. 2.University of Oklahoma73019-0315NormanUSA

Bibliographic information


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)