Hostname: page-component-cd9895bd7-dk4vv Total loading time: 0 Render date: 2024-12-26T21:20:50.474Z Has data issue: false hasContentIssue false
  • English
  • Français

Doubling zeta integrals and local factors for metaplectic groups

Published online by Cambridge University Press:  11 January 2016

Wee Teck Gan
Wee Teck Gan*
Affiliation:
Department of Mathematics, National University of Singapore, Singapore 119076, [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We develop the theory of the doubling zeta integral of Piatetski-Shapiro and Rallis for metaplectic groups Mp2n, and we use it to give precise definitions of the local γ-factors, L-factors, and ε-factors for irreducible representations of Mp2n × GL1, following the footsteps of Lapid and Rallis.

Keywords

11F7022E50
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 208: Memorial Volume for Professor Hiroshi Saito , December 2012 , pp. 67 - 95
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2012

References

[GS] Gan, W. T. and Savin, G., Representations of metaplectic groups I: epsilon dichotomy and local Langlands correspondence, to appear in Compos. Math., available at http://www.math.nus.edu.sg/~matgw/metaplectic-1.pdf (accessed 15 August 2012).Google Scholar
[GPSR] Gelbart, S., Piatetski-Shapiro, I., and Rallis, S., Explicit Constructions of Automorphic L-Functions, Lecture Notes in Math. 1254, Springer, Berlin, 1987.Google Scholar
[LR] Lapid, E. and Rallis, S., “On the local factors of representations of classical groups” in Automorphic Representations, L-Functions and Applications: Progress and Prospects, Ohio State Univ. Math. Res. Inst. Publ. 11, de Gruyter, Berlin, 2005, 309–359.CrossRefGoogle Scholar
[Li] Li, J.-S., Nonvanishing theorems for the cohomology of certain arithmetic quotients, J. Reine Angew. Math. 428 (1992), 177–217.Google Scholar
[MVW] Moeglin, C., Vigneras, M.-F., and Waldspurger, J.-L., Correspondances de Howe sur un corps p-adique, Lecture Notes in Math. 1291, Springer, Berlin, 1987.Google Scholar
[MW] Moeglin, C. and Waldspurger, J.-L., Spectral Decomposition and Eisenstein Series, Cambridge Tracts in Math. 113, Cambridge University Press, Cambridge, 1995.Google Scholar
[PSR] Piatetski-Shapiro, I. and Rallis, S., ε factor of representations of classical groups, Proc. Natl. Acad. Sci. USA 83 (1986), 4589–4593.CrossRefGoogle ScholarPubMed
[R] Rao, R., On some explicit formulas in the theory of the Weil representation, Pacific J. Math. 157 (1993), 335–371.Google Scholar
[Sun] Sun, B. Y., Dual pairs and contragredients of irreducible representations, Pacific J. Math. 249 (2011), 485–494.CrossRefGoogle Scholar
[Sw] Sweet, J., Functional equations of p-adic zeta integrals and representations of the metaplectic group, preprint, 1995.Google Scholar
[Sz] Szpruch, D., The Langlands-Shahidi method for the metaplectic group and applications, preprint, arXiv:1004.3516v1 [math.NT]Google Scholar
[Y] Yamana, S., L-functions and theta correspondences for classical groups, preprint, 2011.Google Scholar
[Z] Zorn, C., Theta dichotomy and doubling epsilon factors for , Amer. J. Math. 133 (2011), 1313–1364.Google Scholar