Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-26T05:40:24.305Z Has data issue: false hasContentIssue false
  • English
  • Français

Meromorphic Continuation of Spherical Cuspidal Data Eisenstein Series

Published online by Cambridge University Press:  20 November 2018

Feryâl Alayont
Feryâl Alayont*
Affiliation:
Department of Mathematics, University of Arizona, 617 N. Santa Rita, Tucson, AZ 85721, U.S.A. email: alayont@math.arizona.edu
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.

Meromorphic continuation of the Eisenstein series induced from spherical, cuspidal data on parabolic subgroups is achieved via reworking Bernstein's adaptation of Selberg's third proof of meromorphic continuation.

Keywords

11F7232N1032D15
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 59 , Issue 6 , 01 December 2007 , pp. 1121 - 1134
Copyright
Copyright © Canadian Mathematical Society 2007

References

[A78] Arthur, J., A trace formula for reductive groups. I. Terms associated to classes in G(Q). Duke Math. J. 45(1978), no. 4, 911–952.Google Scholar
[A80] Arthur, J., A trace formula for reductive groups. II. Applications of a truncation operator. Compositio Math. 40(1980), no. 1, 87–121.Google Scholar
[Ga01a] Garrett, P., Meromorphic continuation of Eisenstein series for SL(2). http://www.math.umn.edu/∼garrett/m/v/mero_contn_eis.ps. Google Scholar
[Ga01b] Garrett, P., The theory of the constant term. http://www.math.umn.edu/∼garrett/m/v/constant_term.ps. Google Scholar
[Ga01c] Garrett, P., Meromorphic continuation of higher-rank Eisenstein series. http://www.math.umn.edu/∼garrett/m/v/tel_aviv_talk.ps.Google Scholar
[Go67] Godement, R., Introduction á la théorie de Langlands. Séminaire Bourbaki 1966/1967, No. 321.Google Scholar
[H83] Hejhal, D. A., The Selberg trace formula for PSL(2, R). Lecture Notes in Mathematics 1001, Springer-Verlag, Berlin, 1983.Google Scholar
[L66] Langlands, R. P., Eisenstein series. In: Algebraic Groups and Discontinuous Subgroups, Proc. Sympos. Pure Math., American Mathematical Society, Providence, RI, 1966, pp. 235–252.Google Scholar
[L76] Langlands, R. P., On the Functional Equations Satisfied by Eisenstein Series. Lecture Notes in Mathematics 544, Springer-Verlag, New York, 1976.Google Scholar
[MW95] Moeglin, C. and Waldspurger, J.-L., Spectral Decomposition and Eisenstein Series: Une Paraphrase de l’ Écriture. Cambridge Tracts in Mathematics 113, Cambridge, Cambridge University Press, 1995.Google Scholar
[R91] Rudin, W., Functional Analysis. Second edition. McGraw-Hill, New York, 1991.Google Scholar
[W90] Wong, S.-T., The Meromorphic Continuation and Functional Equations of Cuspidal Eisenstein Series for Maximal Cuspidal Groups. Mem. Amer.Math. Soc. 83(1990), no. 423.Google Scholar