Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T09:28:06.741Z Has data issue: false hasContentIssue false
  • English
  • Français

On L-Functions of Twisted 3-Dimensional Quaternionic Shimura Varieties

Published online by Cambridge University Press:  11 January 2016

Cristian Virdol
Cristian Virdol*
Affiliation:
Department of Mathematics, Columbia University, 2960 Broadway, New York, NY 10027, U.S.A.
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.

In this paper we compute and continue meromorphically to the entire complex plane the zeta functions of twisted quaternionic Shimura varieties of dimension 3. The twist of the quaternionic Shimura varieties is done by a mod ℘ representation of the absolute Galois group.

Keywords

11F0311F4111F8011R3711R4211R5211R5611R8011S40
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 190 , 2008 , pp. 87 - 104
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2008

References

[B] Blasius, D., Hilbert modular forms and the Ramanujan conjecture, preprint.Google Scholar
[BR] Blasius, D. and Rogawski, J. D., Zeta functions of Shimura varieties, Motives, AMS Proc. Symp. Pure Math. 55, Part 2.Google Scholar
[C] Carayol, H., Sur la mauvaise réduction des courbes de Shimura, Compositio Math ematica, 59 (1986), nr. 2, 151–230.Google Scholar
[HLR] Harder, G., Langlands, R. P. and Rapoport, M., Algebraische Zyclen auf Hilbert-Blumenthal-Flächen, J. Reine Angew. Math., 366 (1986), 53–120.Google Scholar
[I] Ikeda, T., On the location of poles of the triple L-functions, Compositio Math., 83 (1992), 187–237.Google Scholar
[RT] Rogawski, J. D. and Tunnell, J. B., On Artin L-functions associated to Hilbert modular forms of weight one, Inventiones Mathematicae, 74 (1983), 1–43.CrossRefGoogle Scholar
[SE] Serre, J.-P., Linear representations of finite groups, Springer, 1977.Google Scholar
[T] Taylor, R., On Galois representations associated to Hilbert modular forms, Inventiones Matematicae, 98 (1989), 265–280.Google Scholar
[V] Virdol, C., Non-solvable base change for Hilbert modular representations and zeta functions of twisted quaternionic Shimura varieties, preprint; see my web page: http://www.math.columbia.edu/~virdol/.Google Scholar