Local-global principles for representations of quadratic forms

Abstract

We prove the local-global principle holds for the problem of representations of quadratic forms by quadratic forms, in codimension $\ge 7$. The proof uses the ergodic theory of $p$-adic groups, together with a fairly general observation on the structure of orbits of an arithmetic group acting on integral points of a variety.

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References in corpus (2)

• Distribution of periodic torus orbits and Duke's theorem for cubic fields
• Ratner's theorem on SL(2,R)-invariant measures

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• Effective equidistribution and property tau
• On indefinite $k$-universal integral quadratic forms over number fields
• Limiting Distributions of Translates of Divergent Diagonal Orbits
• Averages of Fourier coefficients of Siegel modular forms and representation of binary quadratic forms by quadratic forms in four variables
• Equidistribution of rational subspaces and their shapes
• Effective equidistribution for closed orbits of semisimple groups on homogeneous spaces
• Lecture Notes on Quadratic Forms and their Arithmetic