Finding integral diagonal pairs in a two dimensional -set

Authors:
Lev A. Borisov and Renling Jin

Journal:
Proc. Amer. Math. Soc. **139** (2011), 2431-2434

MSC (2010):
Primary 11B75, 11H06, 11P21

Published electronically:
December 20, 2010

MathSciNet review:
2784808

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Abstract | References | Similar Articles | Additional Information

Abstract: According to Nathanson, an -dimensional -set is a compact subset of such that for every there is with . We prove that every two dimensional -set must contain distinct points such that is in and is neither horizontal nor vertical. This answers a question of P. Hegarty and M. Nathanson.

**1.**M.B. Nathanson,*An inverse problem in number theory and geometric group theory*, in ``Additive Number Theory'', ed. D. Chudnovsky and G. Chudnovsky, Springer, New York, 2010, pp. 249-258.**2.**Z. Ljujic, C. Sanabria,*A note on the inverse problem for the lattice points*, arXiv:1006.5740v1 [math.NT], 29 June 2010.

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Additional Information

**Lev A. Borisov**

Affiliation:
Department of Mathematics, Rutgers University, Piscataway, New Jersey 08854

**Renling Jin**

Affiliation:
Department of Mathematics, College of Charleston, Charleston, South Carolina 29424

DOI:
http://dx.doi.org/10.1090/S0002-9939-2010-10688-3

Received by editor(s):
July 7, 2010

Published electronically:
December 20, 2010

Additional Notes:
The work of the first author was partially supported by NSF Grant 1003445

The work of the second author was partially supported by NSF Grant RUI 0500671.

Communicated by:
Ken Ono

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.