Endpoint restriction estimates for the paraboloid over finite fields
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- by Allison Lewko and Mark Lewko
- Proc. Amer. Math. Soc. 140 (2012), 2013-2028
- DOI: https://doi.org/10.1090/S0002-9939-2011-11444-8
- Published electronically: December 23, 2011
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Abstract:
We prove certain endpoint restriction estimates for the paraboloid over finite fields in three and higher dimensions. Working in the bilinear setting, we are able to pass from estimates for characteristic functions to estimates for general functions while avoiding the extra logarithmic power of the field size which is introduced by the dyadic pigeonhole approach. This allows us to remove logarithmic factors from the estimates obtained by Mockenhaupt and Tao in three dimensions and those obtained by Iosevich and Koh in higher dimensions.References
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Bibliographic Information
- Allison Lewko
- Affiliation: Department of Computer Science, The University of Texas at Austin, Austin, Texas 78701
- Email: alewko@cs.utexas.edu
- Mark Lewko
- Affiliation: Department of Mathematics, The University of Texas at Austin, Austin, Texas 78712
- Email: mlewko@math.utexas.edu
- Received by editor(s): February 4, 2011
- Published electronically: December 23, 2011
- Additional Notes: The first author was supported by a National Defense Science and Engineering Graduate Fellowship
- Communicated by: Michael T. Lacey
- © Copyright 2011
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 140 (2012), 2013-2028
- MSC (2010): Primary 42B10
- DOI: https://doi.org/10.1090/S0002-9939-2011-11444-8
- MathSciNet review: 2888189