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Endpoint restriction estimates for the paraboloid over finite fields


Authors: Allison Lewko and Mark Lewko
Journal: Proc. Amer. Math. Soc. 140 (2012), 2013-2028
MSC (2010): Primary 42B10
DOI: https://doi.org/10.1090/S0002-9939-2011-11444-8
Published electronically: December 23, 2011
MathSciNet review: 2888189
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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.


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Additional 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

DOI: https://doi.org/10.1090/S0002-9939-2011-11444-8
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
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.