Note on a Diophantine inequality in several variables
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- by Jeffrey T. Barton, Hugh L. Montgomery and Jeffrey D. Vaaler PDF
- Proc. Amer. Math. Soc. 129 (2001), 337-345 Request permission
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 $N=1$.References
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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
- MR Author ID: 126550
- Email: hlm@math.lsa.umich.edu
- Jeffrey D. Vaaler
- Affiliation: Department of Mathematics, University of Texas, Austin, Texas 78712
- MR Author ID: 176405
- Email: vaaler@math.utexas.edu
- 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
- © Copyright 2000 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 129 (2001), 337-345
- MSC (2000): Primary 11J25, 11K60, 11K38
- DOI: https://doi.org/10.1090/S0002-9939-00-05795-6
- MathSciNet review: 1800228