Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-11T06:39:02.479Z Has data issue: false hasContentIssue false
  • English
  • Français

Endoscopic $L$-Functions and a Combinatorial Identity

Published online by Cambridge University Press:  20 November 2018

James Arthur
James Arthur*
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario, M5S 3G3
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.

The trace formula contains terms on the spectral side that are constructed from unramified automorphic $L$-functions. We shall establish an identify that relates these terms with corresponding terms attached to endoscopic groups of $G$. In the process, we shall show that the $L$-functions of $G$ that come from automorphic representations of endoscopic groups have meromorphic continuation.

Keywords

22E4522E46
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 51 , Issue 6 , 01 December 1999 , pp. 1135 - 1148
Copyright
Copyright © Canadian Mathematical Society 1999

References

[1] Arthur, J., The trace formula in invariant form. Ann. of Math. (2) 114(1981), 1–74.Google Scholar
[2] Arthur, J., The invariant trace formula I: Local theory. J. Amer. Math. Soc. 1(1988), 323–383.Google Scholar
[3] Arthur, J., The invariant trace formula II: Global theory. J. Amer. Math. Soc. 1(1988), 501–554.Google Scholar
[4] Arthur, J., Unipotent automorphic representations: Global motivation. In: Automorphic Forms, Shimura Varieties, and L-functions, Vol. I, Academic Press, 1–75.Google Scholar
[5] Arthur, J., On local character relations. Selecta Math. 2(1996), 501–579.Google Scholar
[6] Arthur, J., Canonical normalization of weighted characters and a transfer conjecture. C. R. Math. Rep. Acad. Sci. Canada (2) 20(1998), 33–52.Google Scholar
[7] Arthur, J., On the transfer of distributions: weighted orbital integrals. Duke Math. J., to appear.Google Scholar
[8] Arthur, J., A stable trace formula. In preparation.Google Scholar
[9] Kottwitz, R., Stable trace formula: cuspidal tempered terms. Duke Math. J. 51(1984), 611–650.Google Scholar
[10] Langlands, R. P., Problems in the theory of automorphic forms. In: Lecture Notes in Modern Analysis and Applications III, Lecture Notes in Math. 170(1970), 18–86.Google Scholar
[11] Langlands, R. P., On the notion of an automorphic representation. In: Automorphic Forms, Representations and Lfunctions, Part I, Proc. Sympos. Pure Math. 33(1979), 203–207.Google Scholar
[12] Langlands, R. P. and D. Shelstad, On the definition of transfer factors. Math. Ann. 278(1987), 219–271.Google Scholar
[13] Shahidi, F., On the Ramanujan conjecture and finiteness of poles for certain L-functions. Ann. of Math. 127(1988), 547–584.Google Scholar
[14] Shahidi, F., A proof of Langlands’ conjecture on Plancherel measures; Complementary series for p-adic groups. Ann. of Math. 132(1990), 273–330.Google Scholar