Nagoya Mathematical Journal

On $L$-functions of twisted 3-dimensional quaternionic Shimura varieties

Cristian Virdol

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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 $\wp$ representation of the absolute Galois group.

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Nagoya Math. J., Volume 190 (2008), 87-104.

First available in Project Euclid: 23 June 2008

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Zentralblatt MATH identifier

Primary: 11F03: Modular and automorphic functions 11F41: Automorphic forms on GL(2); Hilbert and Hilbert-Siegel modular groups and their modular and automorphic forms; Hilbert modular surfaces [See also 14J20] 11F80: Galois representations 11R37: Class field theory 11R42: Zeta functions and $L$-functions of number fields [See also 11M41, 19F27] 11R52: Quaternion and other division algebras: arithmetic, zeta functions 11R56: Adèle rings and groups 11R80: Totally real fields [See also 12J15] 11S40: Zeta functions and $L$-functions [See also 11M41, 19F27]


Virdol, Cristian. On $L$-functions of twisted 3-dimensional quaternionic Shimura varieties. Nagoya Math. J. 190 (2008), 87--104.

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