Skip to main content
    • Aa
    • Aa


  • S. J. PATTERSON (a1)

The concept of a metaplectic form was introduced about 40 years ago by T. Kubota. He showed how Jacobi-Legendre symbols of arbitrary order give rise to characters of arithmetic groups. Metaplectic forms are the automorphic forms with these characters. Kubota also showed how higher analogues of the classical theta functions could be constructed using Selberg's theory of Eisenstein series. Unfortunately many aspects of these generalized theta series are still unknown, for example, their Fourier coefficients. The analogues in the case of function fields over finite fields can in principle be calculated explicitly and this was done first by J. Hoffstein in the case of a rational function field. Here we shall return to his calculations and clarify a number of aspects of them, some of which are important for recent developments.

Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

6. J. Denef and F. Loeser , Détermination géométrique des sommes de Selberg-Evans, Bull. Soc. Math. France 122 (1994), 533551.

7. J. Denef and F. Loeser , Character sums associated to finite Coxeter groups, Trans. Amer. Math. Soc. 350 (1998), 50475066.

9. J. Hoffstein , Theta functions on the n-fold metaplectic cover of SL(2) – the function field case, Inv. Math. 107 (1992), 6186.

10. D. A. Kazhdan and S. J. Patterson , Metaplectic forms, Publ. Math. IHES 59 (1984), 35142.

Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
Please enter your name
Please enter a valid email address
Who would you like to send this to? *



Full text views

Total number of HTML views: 0
Total number of PDF views: 3 *
Loading metrics...

Abstract views

Total abstract views: 37 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 28th May 2017. This data will be updated every 24 hours.