Near arithmetic progressions in sparse sets
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- by Steven C. Leth PDF
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Abstract:
Nonstandard methods are used to obtain results in combinatorial number theory. The main technique is to use the standard part map to translate density properties of subsets of $^{\ast }\mathbb {N}$ into Lebesgue measure properties on $[0,1]$. This allows us to obtain a simple condition on a standard sequence $A$ that guarantees the existence of intervals in arithmetic progression, all of which contain elements of $A$ with various uniform density conditions.References
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Additional Information
- Steven C. Leth
- Affiliation: Department of Mathematical Sciences, University of Northern Colorado, Greeley, Colorado 80639
- Email: steven.leth@unco.edu
- Received by editor(s): August 31, 2004
- Received by editor(s) in revised form: October 14, 2004, November 7, 2004, and January 5, 2005
- Published electronically: December 2, 2005
- Additional Notes: The author thanks the referee for identifying several errors in the original version
- Communicated by: Carl G. Jockusch, Jr.
- © Copyright 2005
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 134 (2006), 1579-1589
- MSC (2000): Primary 11B25, 11B05, 03H05, 03H15
- DOI: https://doi.org/10.1090/S0002-9939-05-08141-4
- MathSciNet review: 2204267