Approximate polynomial structure in additively large sets

Di Nasso, Mauro and Goldbring, Isaac and Jin, Renling and Leth, Steven and Lupini, Martino and Mahlburg, Karl (2016) Approximate polynomial structure in additively large sets. Integers, 16 . Art. No. A49. ISSN 1553-1732. http://resolver.caltech.edu/CaltechAUTHORS:20161004-084936564

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Abstract

We show that any subset of the natural numbers with positive logarithmic Banach density contains a set that is within a factor of two of a geometric progression, improving the bound on a previous result of the authors. Density conditions on subsets of the natural numbers that imply the existence of approximate powers of arithmetic progressions are developed and explored.

Item Type:

Article

Related URLs:

URL	URL Type	Description
http://www.integers-ejcnt.org/vol16.html	Publisher	Journal Volume
https://arxiv.org/abs/1508.02350	arXiv	Discussion Paper

ORCID:

Author	ORCID
Lupini, Martino	0000-0003-1588-7057

Additional Information:

© 2016 The Aurhors. Received: 8/10/15, Accepted: 6/15/16, Published: 7/7/16. I. Goldbring was partially supported by NSF CAREER grant DMS-1349399. M. Lupini was supported by the York University Susan Mann Dissertation Scholarship and by the ERC Starting grant no. 259527 of Goulnara Arzhantseva. K. Mahlburg was supported by NSF Grant DMS-1201435. This work was initiated during a week-long meeting at the American Institute for Mathematics on August 4-8, 2014 as part of the SQuaRE (Structured Quartet Research Ensemble) project “Nonstandard Methods in Number Theory.” The authors would like to thank the Institute for the opportunity and for the Institute’s hospitality during their stay.

Funders:

Funding Agency	Grant Number
NSF	DMS-1349399
York University	UNSPECIFIED
European Research Council (ERC)	259527
NSF	DMS-1201435

Record Number:

CaltechAUTHORS:20161004-084936564

Persistent URL:

http://resolver.caltech.edu/CaltechAUTHORS:20161004-084936564

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No commercial reproduction, distribution, display or performance rights in this work are provided.

ID Code:

70793

Collection:

CaltechAUTHORS

Deposited By:

Tony Diaz

Deposited On:

04 Oct 2016 18:31

Last Modified:

27 Apr 2017 19:49

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