On growth in an abstract plane

Nick Gill; H. A. Helfgott; Misha Rudnev

doi:10.1090/proc/12309

On growth in an abstract plane

Nick Gill, H. A. Helfgott, Misha Rudnev

Research output: Contribution to journal › Article (Academic Journal) › peer-review

3 Citations (Scopus)

228 Downloads (Pure)

Abstract

There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over R or C, geometric statements on growth often have geometric proofs, what little is known over finite fields rests on arithmetic proofs.

We discuss strategies for geometric proofs of growth over finite fields, and show that growth can be defined and proven in an abstract projective plane - even one with weak axioms.

Original language	Undefined/Unknown
Pages (from-to)	3593-3602
Number of pages	10
Journal	Proceedings of the American Mathematical Society
Volume	143
Early online date	13 Apr 2015
DOIs	https://doi.org/10.1090/proc/12309
Publication status	Published - 20 Dec 2015

Bibliographical note

10 pages

Keywords

math.CO
51E15 (primary)
11B30 (secondary)
51A35

Access to Document

10.1090/proc/12309

Full-text PDF (accepted author manuscript)
This is the accepted author manuscript (AAM). The final published version (version of record) is available online via American Mathematical Society at http://dx.doi.org/10.1090/proc/12309. Please refer to any applicable terms of use of the publisher.
Accepted author manuscript, 154 KB

Handle.net

Persistent link

Cite this

@article{c59440f728c343debb678b6efb5ce09c,

title = "On growth in an abstract plane",

abstract = "There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over R or C, geometric statements on growth often have geometric proofs, what little is known over finite fields rests on arithmetic proofs.We discuss strategies for geometric proofs of growth over finite fields, and show that growth can be defined and proven in an abstract projective plane - even one with weak axioms.",

keywords = "math.CO, 51E15 (primary), 11B30 (secondary), 51A35",

author = "Nick Gill and Helfgott, {H. A.} and Misha Rudnev",

note = "10 pages",

year = "2015",

month = dec,

day = "20",

doi = "10.1090/proc/12309",

language = "Undefined/Unknown",

volume = "143",

pages = "3593--3602",

journal = "Proceedings of the American Mathematical Society",

issn = "0002-9939",

publisher = "American Mathematical Society",

}

TY - JOUR

T1 - On growth in an abstract plane

AU - Gill, Nick

AU - Helfgott, H. A.

AU - Rudnev, Misha

N1 - 10 pages

PY - 2015/12/20

Y1 - 2015/12/20

N2 - There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over R or C, geometric statements on growth often have geometric proofs, what little is known over finite fields rests on arithmetic proofs.We discuss strategies for geometric proofs of growth over finite fields, and show that growth can be defined and proven in an abstract projective plane - even one with weak axioms.

AB - There is a parallelism between growth in arithmetic combinatorics and growth in a geometric context. While, over R or C, geometric statements on growth often have geometric proofs, what little is known over finite fields rests on arithmetic proofs.We discuss strategies for geometric proofs of growth over finite fields, and show that growth can be defined and proven in an abstract projective plane - even one with weak axioms.

KW - math.CO

KW - 51E15 (primary)

KW - 11B30 (secondary)

KW - 51A35

U2 - 10.1090/proc/12309

DO - 10.1090/proc/12309

M3 - Article (Academic Journal)

SN - 0002-9939

VL - 143

SP - 3593

EP - 3602

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

ER -