On an exact mass formula of Shimura

On an exact mass formula of Shimura

Wee Teck Gan, Jonathan P. Hanke, and Jiu-Kang Yu

Source: Duke Math. J. Volume 107, Number 1 (2001), 103-133.

Abstract

In a series of recent papers, G. Shimura obtained an exact formula for the mass of a maximal lattice in a quadratic or hermitian space over a totally real number field. Using Bruhat-Tits theory, we obtain a quick and more conceptual proof of his formula when the form is totally definite.

Primary Subjects: 11E57

Secondary Subjects: 11E41, 20G35

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1091736138
Mathematical Reviews number (MathSciNet): MR1815252
Digital Object Identifier: doi:10.1215/S0012-7094-01-10716-3
Zentralblatt MATH identifier: 1023.11019

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References

F. Bruhat and J. Tits, Groupes réductifs sur un corps local, II: Schémas en groupes; existence d'une donnée radicielle valuée, Inst. Hautes Études Sci. Publ. Math. 60 (1984), 197--376.

Mathematical Reviews (MathSciNet): MR756316

--. --. --. --., Schémas en groupes et immeubles des groupes classiques sur un corps local, II: Groupes unitaires, Bull. Soc. Math. France 115 (1987), 141--195.

Mathematical Reviews (MathSciNet): MR919421

B. H. Gross, On the motive of a reductive group, Invent. Math. 130 (1997), 287--313.

Mathematical Reviews (MathSciNet): MR1474159

Digital Object Identifier: doi:10.1007/s002220050186

B. H. Gross and W. T. Gan, Haar measure and the Artin conductor, Trans. Amer. Math. Soc. 351 (1999), 1691--1704.

Mathematical Reviews (MathSciNet): MR1458303

Digital Object Identifier: doi:10.1090/S0002-9947-99-02095-4

JSTOR: links.jstor.org

R. Kottwitz, Tamagawa numbers, Ann. of Math. (2) 127 (1988), 629--.\hs646.

Mathematical Reviews (MathSciNet): MR942522

Digital Object Identifier: doi:10.2307/2007007

JSTOR: links.jstor.org

A. Moy and G. Prasad, Unrefined minimal $K$-types for $p$-adic groups, Invent. Math. 116 (1994), 393--.\hs408.

Mathematical Reviews (MathSciNet): MR1253198

Digital Object Identifier: doi:10.1007/BF01231566

A. Moy and G. Prasad, Jacquet functors and unrefined minimal $K$-types, Comment. Math. Helv. 71 (1996), 98--121.

Mathematical Reviews (MathSciNet): MR1371680

Digital Object Identifier: doi:10.1007/BF02566411

T. Ono, ``On Tamagawa numbers'' in Algebraic Groups and Discontinuous Subgroups (Boulder, Colo., 1965), Proc. Sympos. Pure Math. 9, Amer. Math. Soc., Providence, 1966, 122--132.

Mathematical Reviews (MathSciNet): MR209290

G. Prasad, Volumes of $S$-arithmetic quotients of semisimple groups, Inst. Hautes Études Sci. Publ. Math. 69 (1989), 91--117.

Mathematical Reviews (MathSciNet): MR1019962

Digital Object Identifier: doi:10.1007/BF02698841

G. Shimura, Euler Products and Eisenstein Series, CBMS Reg. Conf. Ser. Math. 93, Amer. Math. Soc., Providence, 1997.

Mathematical Reviews (MathSciNet): MR1450866

--. --. --. --., An exact mass formula for orthogonal groups, Duke Math. J. 97 (1999), 1--.\hs66.

Mathematical Reviews (MathSciNet): MR1681092

Digital Object Identifier: doi:10.1215/S0012-7094-99-09701-6

Project Euclid: euclid.dmj/1077228500

--. --. --. --., Some exact formulas on quaternion unitary groups, J. Reine Angew. Math. 509 (1999), 67--102.

Mathematical Reviews (MathSciNet): MR1679167

J.-P. Serre, Local Fields, Grad. Texts in Math. 67, Springer, New York, 1979.

Mathematical Reviews (MathSciNet): MR554237

J. Tits, ``Reductive groups over local fields'' in Automorphic Forms, Representations, and L-functions, I (Oregon State Univ., Corvallis, 1977), Proc. Sympos. Pure Math. 33, Amer. Math. Soc., Providence, 1979, 29--.\hs69

Mathematical Reviews (MathSciNet): MR546588

J.-K. Yu, Construction of tame supercuspidal representations, to appear in J. Amer. Math. Soc.

Mathematical Reviews (MathSciNet): MR1824988

Digital Object Identifier: doi:10.1090/S0894-0347-01-00363-0

JSTOR: links.jstor.org

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