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Local-global principles for representations of quadratic forms

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Abstract

We prove a local-global principle for the problem of representations of quadratic forms by quadratic forms over ℤ, in codimension ≥5. 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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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin, 323 Van Vleck Hall, 480 Lincoln Drive, Madison, WI, 53706, USA

    Jordan S. Ellenberg

  2. Courant Institute of Mathematical Sciences, New York University, 251 Mercer Street, New York, NY, 10012-1185, USA

    Akshay Venkatesh

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  1. Jordan S. Ellenberg
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  2. Akshay Venkatesh
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Correspondence to Akshay Venkatesh.

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Ellenberg, J., Venkatesh, A. Local-global principles for representations of quadratic forms. Invent. math. 171, 257–279 (2008). https://doi.org/10.1007/s00222-007-0077-7

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  • DOI: https://doi.org/10.1007/s00222-007-0077-7

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