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

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

We establish estimates for the number of points that belong to an aligned box in in terms of certain exponential sums. These generalize previous results that were known only in case .

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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:
https://doi.org/10.1090/S0002-9939-00-05795-6

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