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

 

Note on a Diophantine inequality in several variables


Authors: Jeffrey T. Barton, Hugh L. Montgomery and Jeffrey D. Vaaler
Journal: Proc. Amer. Math. Soc. 129 (2001), 337-345
MSC (2000): Primary 11J25, 11K60, 11K38
Published electronically: August 28, 2000
MathSciNet review: 1800228
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Abstract | References | Similar Articles | Additional Information

Abstract:

We establish estimates for the number of points that belong to an aligned box in $(\mathbb{R}/\mathbb{Z})^N$ in terms of certain exponential sums. These generalize previous results that were known only in case $N=1$.


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Additional Information

Jeffrey T. Barton
Affiliation: Department of Mathematics, Birmingham-Southern College, Birmingham, Alabama 35254
Email: jbarton@bsc.edu

Hugh L. Montgomery
Affiliation: Department of Mathematics, University of Michigan, Ann Arbor, Michigan 48109
Email: hlm@math.lsa.umich.edu

Jeffrey D. Vaaler
Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
Email: vaaler@math.utexas.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05795-6
PII: S 0002-9939(00)05795-6
Received by editor(s): April 15, 1999
Published electronically: August 28, 2000
Additional Notes: The first and third authors’ research was supported in part by the National Science Foundation (DMS-9622556) and the Texas Advanced Research Project.
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 2000 American Mathematical Society