An introduction to $Γ$-number fields

Average Representation Numbers For Spinor Genera

In this paper we establish a formula for the average of representation numbers of ternary quadratic forms in a spinor genus over a totally real number field. The significant fact about the formula is the fact that it is given in terms of local quantities. Such a formula has already been established by Kneser, Hsia, and Schulze-Pillot, by a different method.

Spinor norm for skew-hermitian forms over quaternion algebras

We complete all local spinor norm computations for quaternionic skew-hermitian forms over the field of rational numbers. Examples of class number computations are provided.

Spinor class field for generalized Eichler orders

We compute the spinor class field for a genus of orders, in a central simple algebra of higher dimension, that are intersections of two maximal orders. In particular, we compute the number of spinor genera in a genus of such orders, as the degree of an explicit extension of class fields.

二元局部域上相对整数旋量范数群

Relative integral spinor norm groups over dyadic local fields

本文研究了局部二元域上相对整数旋量范数群的显式公式。

Spinor class fields for sheaves of lattices

We extend the theory of spinor class field and representation fields previously defined for lattices over the ring of integers of a number field to both, lattices over the coordinate ring of a smooth irreducible affine curve over a finite field, and sheaves of lattices over the structure sheaf of an irreducible smooth projective curve over a finite field.