Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

   

 

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
Published electronically: December 23, 2011
MathSciNet review: 2888189
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 42B10

Retrieve articles in all journals with MSC (2010): 42B10


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: http://dx.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.



Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia