Geometric properties of points on modular hyperbolas
Authors:
Kevin Ford, Mizan R. Khan and Igor E. Shparlinski
Journal:
Proc. Amer. Math. Soc. 138 (2010), 41774185
MSC (2010):
Primary 11A07; Secondary 11H06, 11N69
Published electronically:
July 9, 2010
MathSciNet review:
2680044
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Additional Information
Abstract: Given an integer , let be the set and let be the maximal difference of for . We prove that for almost all , We also improve some previously known upper and lower bounds on the number of vertices of the convex closure of .
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Additional Information
Kevin Ford
Affiliation:
Department of Mathematics, University of Illinois at UrbanaChampaign, 1409 West Green Street, Urbana, Illinois 61801
Email:
ford@math.uiuc.edu
Mizan R. Khan
Affiliation:
Department of Mathematics and Computer Science, Eastern Connecticut State University, Willimantic, Connecticut 06226
Email:
khanm@easternct.edu
Igor E. Shparlinski
Affiliation:
Department of Computing, Macquarie University, Sydney, NSW 2109, Australia
Email:
igor@ics.mq.edu.au
DOI:
http://dx.doi.org/10.1090/S000299392010105610
PII:
S 00029939(2010)105610
Received by editor(s):
February 11, 2010
Published electronically:
July 9, 2010
Additional Notes:
The research of the first author was supported in part by NSF grants DMS0555367 and DMS0901339.
The research of the third author was supported by ARC grants DP0556431 and DP1092835.
Communicated by:
Matthew A. Papanikolas
Article copyright:
© Copyright 2010 American Mathematical Society
