Local densities of 2-adic quadratic forms☆
Local densities of 2-adic quadratic forms☆
复制标题
DOI：
10.1016/j.jnt.2004.05.002
复制
发表时间：
2004-10
影响因子：
0.7
通讯作者：
Tonghai Yang
中科院分区：
文献类型：
--
作者：
Tonghai Yang
本文给出了Z2上二次2-整格L表示2 × 2 2-整矩阵T的局部密度数的一个显式公式。非二元的情况下，处理在以前的文件。当L是Q2上四元数代数的迹零元空间中的（极大）格时的特殊情况产生了一个干净而有趣的公式，它与非并元情况在Gross-Keating不变量方面完全匹配。本文与Kudla和Rapoport共同研究了一类亏格为2的Eisenstein级数的中心导数与某条Shimura曲线上算术0-圈的母函数的关系。
In this paper, we give an explicit from formula for the local density number of representing a two by two 2-integral matrix T by a quadratic 2-integral lattice L over Z2. The non-dyadic case was dealt in a previous paper. The special case when L is a (maximal) lattice in the space of trace zero elements in a quaternion algebra over Q2yields a clean and interesting formula, which matches up perfectly with the non-dyadic case in terms of the Gross–Keating invariants. This work is used to compare the central derivative of a genus two Eisenstein series with certain generating function of arithmetic 0-cycles on certain Shimura curve, in a joint work with Kudla and Rapoport.