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

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

back to Table of Contents

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

previous :: next