On the volume set of point sets in vector spaces over finite fields

Author:
Le Anh Vinh

Journal:
Proc. Amer. Math. Soc. **141** (2013), 3067-3071

MSC (2010):
Primary 11T99

Published electronically:
June 4, 2013

MathSciNet review:
3068960

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Abstract | References | Similar Articles | Additional Information

Abstract: We show that if is a subset of the -dimensional vector space over a finite field () of cardinality , then the set of volumes of -dimensional parallelepipeds determined by covers . This bound is sharp up to a factor of , as taking to be a -hyperplane through the origin shows.

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Additional Information

**Le Anh Vinh**

Affiliation:
University of Education, Vietnam National University, Hanoi, Vietnam

Email:
vinhla@vnu.edu.vn

DOI:
http://dx.doi.org/10.1090/S0002-9939-2013-11630-8

Received by editor(s):
October 1, 2011

Received by editor(s) in revised form:
December 5, 2011

Published electronically:
June 4, 2013

Additional Notes:
This research is supported by the Vietnam National Foundation for Science and Technology Development, grant No. 101.01-2011.28

Communicated by:
Jim Haglund

Article copyright:
© Copyright 2013
American Mathematical Society