6 papers · 1 filter
Single conjugacy classes of isometries in orthogonal groups over local fields
Fei Xu, Bo Zhang
All isometries in a quadratic space over a non-archimedean local field of characteristic not 2 satisfying that any isometry which is conjugate to in the general linear…
Integral embeddings of central simple algebras over number fields
Jiaqi Xie, Fei Xu
A criterion for determining exactly when an order of a maximal subfield of a central simple algebra over a number field can be embedded into an order of this algebra is given. Vari…
Counting integral points on indefinite ternary quadratic equations over number fields
Fei Xu, Runlin Zhang
We study an asymptotic formula for counting integral points over an equation defined by a non-degenerated indefinite integral ternary quadratic form representing a non-zero int…
Brauer-Manin obstruction for Markoff surfaces
J. -L. Colliot-Thélène, Dasheng Wei, Fei Xu
Ghosh and Sarnak have studied integral points on surfaces defined by an equation x^2+y^2+z^2-xyz= m over the integers. For these affine surfaces, we systematically study the Brauer…
Strong approximation for a family of norm varieties
Yang Cao, Dasheng Wei, Fei Xu
We study strong approximation of the equation N_{L/k}(x) = \prod_{i=1}^n p_i(t) where L/k is a finite extension of number fields and p_i(t)'s are distinct irreducible polynomials o…
Counting Integral Points in Certain Homogeneous Spaces
Dasheng Wei, Fei Xu
The asymptotic formula of the number of integral points in non-compact symmetric homogeneous spaces of semi-simple simply connected algebraic groups is given by the average of the…