Functiones et Approximatio Commentarii Mathematici

The meromorphic continuation of the zeta function of Siegel modular threefolds over totally real fields

Cristian Virdol

Full-text: Open access


In this paper we prove the meromorphic continuation of the zeta function of Siegel modular threefolds over arbitrary totally real number fields.

Article information

Funct. Approx. Comment. Math., Volume 47, Number 2 (2012), 143-148.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20]
Secondary: 11F80: Galois representations 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 11R80: Totally real fields [See also 12J15]

Siegel threefolds totally real fields meromorphic continuation


Virdol, Cristian. The meromorphic continuation of the zeta function of Siegel modular threefolds over totally real fields. Funct. Approx. Comment. Math. 47 (2012), no. 2, 143--148. doi:10.7169/facm/2012.47.2.2.

Export citation


  • T. Barnet-Lamb, T. Gee, D. Geraghty, R. Taylor, Potential automorphy and change of weight, preprint.
  • C.W. Curtis, I. Reiner, Methods of Representation Theory, Vol. I, Wiley, New York, 1981.
  • P. Deligne, Travaux de Shimura, Sém. Bourbaki Féb. 71, Exposé 389, Lectures Notes in Math. vol. 244. Berlin-Heidelberg-New York; Springer 1971.
  • G.Harder, R.P. Langlands, M.Rapoport, Algebraische Zyklen auf Hilbert-Blumenthal-Flächen, J. Reine Angew. Math. 366 (1986), 53–120.
  • C. Skinner, E. Urban, Sur les déformations p-adiques de certaines représentations automorphes, J. Inst. Math. Jussieu 5 (2006), no. 4, 629–698.
  • R. Taylor, On the l-adic cohomology of Siegel threefolds, Invent. Math. 114 (1993), no. 2, 289–310.
  • C. Virdol, Base change and the Birch and Swinnerton-Dyer conjecture, Functiones et Approximatio, Commentarii Mathematici, to appear.
  • C. Virdol, The meromorphic continuation of the zeta function of a product of Hilbert and Picard modular surfaces over CM-fields, submitted.
  • R. Weissauer, Differentialformen zu Untergruppen der Siegelschen Modulgruppe zweiten Grades, J. Reine Angew. Math. 391 (1988), 100–156.
  • R. Weissauer, The Picard group of Siegel modular threefolds, J. Reine Angew. Math. 430 (1992), 179–211.
  • R. Weissauer, Endoscopy for GSp(4) and the cohomology of Siegel modular threefolds, Lecture Notes in Mathematics, 1968. Springer-Verlag, Berlin, 2009.
  • R. Weissauer, Four dimensional Galois representations. Formes automorphes. II. Le cas du groupe GSp(4) Astérisque No. 302 (2005), 67–150.