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The discretized sum-product and projection theorems

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Abstract

We give a new presentation of the discrete ring theorem for sets of real numbers [B]. Special attention is given to the relation between the various parameters. As an application, new Marstrand type projection theorems are obtained and formulated either in terms of box or Hausdorff dimension. It is shown that the dimension of the projections satisfies a nontrivial lower bound outside a very sparse set of exceptional directions.

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Authors and Affiliations

  1. Institute for Advanced Study, School of Mathematics, Princeton, NJ, 08540, USA

    Jean Bourgain

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  1. Jean Bourgain
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Correspondence to Jean Bourgain.

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Bourgain, J. The discretized sum-product and projection theorems. JAMA 112, 193–236 (2010). https://doi.org/10.1007/s11854-010-0028-x

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  • DOI: https://doi.org/10.1007/s11854-010-0028-x

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