Arithmetic volumes for lattices over p-adic rings

被引：1

作者：

Fiori, Andrew ^{[1
]}

机构：

[1] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

来源：

JOURNAL OF NUMBER THEORY | 2014年 / 141卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Local densities; Orthogonal group; Arithmetic volume; Representation densities; Lattices; QUADRATIC-FORMS; LOCAL-DENSITIES; PROPORTIONALITY;

D O I：

10.1016/j.jnt.2014.02.011

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we develop formulas for computing the arithmetic volume of orthogonal groups for lattices over the maximal orders of finite extensions of Z(p). We specifically develop new explicit formulas for unimodular lattices over 2-adic rings. We also develop a reduction of the general problem to that of unimodular lattices together with the combinatorial problem of computing representatives for all possible Jordan decompositions. (C) 2014 Elsevier Inc. All rights reserved.

引用

页码：343 / 374

页数：32

共 25 条

[1]

[Anonymous], 1993, CAMBRIDGE TRACTS MAT

[2] LOW-DIMENSIONAL LATTICES .4. THE MASS FORMULA [J].

CONWAY, JH ;

SLOANE, NJA .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1988, 419 (1857) :259-286

[3]

Fiori A., 2013, THESIS MCGILL U

[4]

Gan WT, 2000, DUKE MATH J, V105, P497

[5]

Gritsenko V, 2008, DOC MATH, V13, P1

[6] ON THE INTERSECTION OF MODULAR CORRESPONDENCES [J].

GROSS, BH ;

KEATING, K .

INVENTIONES MATHEMATICAE, 1993, 112 (02) :225-245

[7] Algebraic modular forms [J].

Gross, BH .

ISRAEL JOURNAL OF MATHEMATICS, 1999, 113 (1) :61-93

[8]

Hanke J, 2005, J REINE ANGEW MATH, V584, P1

[9] An explicit formula for Siegel series [J].

Katsurada, H .

AMERICAN JOURNAL OF MATHEMATICS, 1999, 121 (02) :415-452

[10]

Kneser M, 2002, Quadratische Formen. Neu bearbeitet und herausgegeben in Zusammenarbeit mit Rudolf Scharlau

← 1 2 3 →