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Density of integer solutions to diagonal quadratic forms

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Abstract.

Let Q be a non-singular diagonal quadratic form in at least four variables. We provide upper bounds for the number of integer solutions to the equation Q = 0, which lie in a box with sides of length 2B, as B → ∞. The estimates obtained are completely uniform in the coefficients of the form, and become sharper as they grow larger in modulus.

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Authors and Affiliations

  1. University of Bristol, England

    T. D. Browning

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  1. T. D. Browning
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Browning, T. Density of integer solutions to diagonal quadratic forms. Mh Math 152, 13–38 (2007). https://doi.org/10.1007/s00605-007-0457-5

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  • DOI: https://doi.org/10.1007/s00605-007-0457-5

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