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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:
URLURL TypeDescription
http://www.integers-ejcnt.org/vol16.htmlPublisherJournal Volume
https://arxiv.org/abs/1508.02350arXivDiscussion Paper
ORCID:
AuthorORCID
Lupini, Martino0000-0003-1588-7057
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 AgencyGrant Number
NSFDMS-1349399
York UniversityUNSPECIFIED
European Research Council (ERC)259527
NSFDMS-1201435
Record Number:CaltechAUTHORS:20161004-084936564
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20161004-084936564
Usage Policy: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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