We give an explicit formula for local densities of integral representations of nondegenerate integral symmetric matrices of arbitrary size in the case p{2, in terms of invariants of quadratic forms.
On orthogonal groups over the integers of a non-dyadic local field
β Scribed by Yoshio Mimura
- Publisher
- Elsevier Science
- Year
- 1981
- Tongue
- English
- Weight
- 215 KB
- Volume
- 13
- Category
- Article
- ISSN
- 0022-314X
No coin nor oath required. For personal study only.
π SIMILAR VOLUMES
Let O denote the ring of integers of a local field. In this note we prove an Γ 4 Ο± approximation theorem for the Riesz type kernels β₯ over O. The proof , , n ns1 Ε½ . y1 requires a sharp estimate of the Dirichlet kernel D x on P \_ O, which may also n have independent interest. As a consequence we so
Let O O be the ring of integers in a local field K. We solve an open problem due Ε½ to M. H. Taibleson 1975, ''Math. Notes,'' Vol. 15, Princeton Univ. Press, Prince-. 1 Ε½ . ton, NJ : Suppose f g L O O . Does the Cesaro means of f converge to f almost `Ε½ p p . everywhere if K has characteristic zero?