Local densities of 2-adic quadratic forms

✍ Scribed by Tonghai Yang

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 514 KB
• Volume: 108
• Category: Article
• ISSN: 0022-314X
• DOI: 10.1016/j.jnt.2004.05.002

✦ Synopsis

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 Z 2 : 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 Q 2 yields 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.