Add to ORKGIn this survey paper, we discuss the classical Cassels\u27 theorem on existence of small-height zeros of quadratic forms over Q and its many extensions, to different fields and rings, as well as to more general situations, such as existence of totally isotropic small-height subspaces. We also discuss related recent results on effective structural theorems for quadratic spaces, as well as Cassels\u27-type theorems for small-height zeros of quadratic forms with additional conditions. We conclude with a selection of open problems
textWe treat a few related problems about the existence of algebraic points of small height that sa...
textWe treat a few related problems about the existence of algebraic points of small height that sa...
textIn 1955, Cassels proved a now celebrated theorem giving a search bound algorithm for determining...
A celebrated theorem of Cassels (1955) asserts that an integral quadratic form, which is isotropic o...
A celebrated theorem of Cassels (1955) asserts that an integral quadratic form, which is isotropic o...
A classical theorem of Cassels (1955) asserts that if an integral quadratic form is isotropic over ...
In 1955 J. W. S. Cassels proved that if an integral quadratic form has a non-trivial rational zero t...
In 1955 J. W. S. Cassels proved that if an integral quadratic form has a non-trivial rational zero t...
In this talk, I will discuss a variety of results on existence of points and subspaces of bounded he...
Abstract. Let K be a global field or Q, F a nonzero quadratic form on KN, N ≥ 2, and V a subspace of...
In this paper we establish three results on small-height zeros of quadratic polynomials over Q. For ...
Let K be a global field or Q, F a nonzero quadratic form on KN , N ≥ 2, and V a subspace of KN . We ...
Let be a quadratic form in variables defined on a vector space over a global field , and be a fi...
In this paper we establish three results on small-height zeros of quadratic polynomials over Q. For ...
Abstract. Given an arbitrary n, we consider anisotropic quadratic forms of dimension n over all fiel...
textWe treat a few related problems about the existence of algebraic points of small height that sa...
textWe treat a few related problems about the existence of algebraic points of small height that sa...
textIn 1955, Cassels proved a now celebrated theorem giving a search bound algorithm for determining...
A celebrated theorem of Cassels (1955) asserts that an integral quadratic form, which is isotropic o...
A celebrated theorem of Cassels (1955) asserts that an integral quadratic form, which is isotropic o...
A classical theorem of Cassels (1955) asserts that if an integral quadratic form is isotropic over ...
In 1955 J. W. S. Cassels proved that if an integral quadratic form has a non-trivial rational zero t...
In 1955 J. W. S. Cassels proved that if an integral quadratic form has a non-trivial rational zero t...
In this talk, I will discuss a variety of results on existence of points and subspaces of bounded he...
Abstract. Let K be a global field or Q, F a nonzero quadratic form on KN, N ≥ 2, and V a subspace of...
In this paper we establish three results on small-height zeros of quadratic polynomials over Q. For ...
Let K be a global field or Q, F a nonzero quadratic form on KN , N ≥ 2, and V a subspace of KN . We ...
Let be a quadratic form in variables defined on a vector space over a global field , and be a fi...
In this paper we establish three results on small-height zeros of quadratic polynomials over Q. For ...
Abstract. Given an arbitrary n, we consider anisotropic quadratic forms of dimension n over all fiel...
textWe treat a few related problems about the existence of algebraic points of small height that sa...
textWe treat a few related problems about the existence of algebraic points of small height that sa...
textIn 1955, Cassels proved a now celebrated theorem giving a search bound algorithm for determining...