KAKEYA-TYPE SETS IN LOCAL FIELDS WITH FINITE RESIDUE FIELD. Issue 2 (17th February 2016)

• Record Type: Journal Article
• Authors: Fraser, Robert
• Is Part Of: Mathematika. Volume 62:Issue 2(2016)
• Page Start: 614
• Page End: 629
• Publication Date: 2016-02-17
• Subjects: 28A75 (primary); Mathematics -- Periodicals; 510.5
• DOI: 10.1112/S0025579315000388
• Languages: English
• ISSNs: 0025-5793

Abstract

Abstract : We present a construction of a measure-zero Kakeya-type set in a finite-dimensional space $K^{n}$ over a local field with finite residue field. The construction is an adaptation of the ideas appearing in works by Sawyer [ Mathematika 34 (1) (1987), 69–76] and Wisewell [ Mathematika 51 (1–2) (2004), 155–162]. The existence of measure-zero Kakeya-type sets over discrete valuation rings is also discussed, giving an alternative construction to the one over $\mathbb{F}_{\ell }\unicode[STIX]{x27E6}t\unicode[STIX]{x27E7}$ presented by Dummit and Hablicsek [ Mathematika 59 (2) (2013), 257–266].