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Shimura Varieties and the Selberg Trace Formula

Published online by Cambridge University Press:  20 November 2018

R. P. Langlands
R. P. Langlands*
Affiliation:
Institute for Advanced Study, Princeton, New Jersey
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This paper is a report on work in progress rather than a description of theorems which have attained their final form. The results I shall describe are part of an attempt to continue to higher dimensions the study of the relation between the Hasse-Weil zeta-functions of Shimura varieties and the Euler products associated to automorphic forms, which was initiated by Eichler, and extensively developed by Shimura for the varieties of dimension one bearing his name. The method used has its origins in an idea of Sato, which was exploited by Ihara for the Shimura varieties associated to GL(2).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 6 , 01 December 1977 , pp. 1292 - 1299
Copyright
Copyright © Canadian Mathematical Society 1977

References

1. Deligne, P., Variétés abéliennes ordinaires sur un corps fini, Inv. Math. 8 (1969), 238–243.Google Scholar
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3. Ihara, Y., Hecke polynomials as congruence Ç junctions in elliptic modular case, Ann. of Math. 85 (1967), 267–295.Google Scholar
4. Ihara, Y. On congruence monodromy problems, University of Tokyo (1969).Google Scholar
5. Langlands, R. P., Some contemporary problems with origins in the Jugendtraum, in Mathematical developments arising from Hilbert problems, Amer. Math. Soc. (1976), 401–418.Google Scholar