Applications of the sum-product theorem in finite fields

Avi Wigderson

doi:10.1109/CCC.2006.9

Applications of the sum-product theorem in finite fields

Avi Wigderson^*

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

Abstract

About two years ago Bourgain, Katz and Tao [1] proved the following theorem, essentially stating that in every finite field, a set which does not grow much when we add all pairs of elements, and when we multiply all pairs of elements, must be very close to a subfield.

Original language	English
Title of host publication	Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006
Pages	111
Number of pages	1
DOIs	https://doi.org/10.1109/CCC.2006.9
State	Published - 2006
Externally published	Yes
Event	21st Annual IEEE Conference on Computational Complexity, CCC 2006 - Prague, Czech Republic Duration: 16 Jul 2006 → 20 Jul 2006

Publication series

Name	Proceedings of the Annual IEEE Conference on Computational Complexity
Volume	2006
ISSN (Print)	1093-0159

Conference

Conference	21st Annual IEEE Conference on Computational Complexity, CCC 2006
Country/Territory	Czech Republic
City	Prague
Period	16/07/06 → 20/07/06

Access to Document

10.1109/CCC.2006.9

Cite this

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title = "Applications of the sum-product theorem in finite fields",

abstract = "About two years ago Bourgain, Katz and Tao [1] proved the following theorem, essentially stating that in every finite field, a set which does not grow much when we add all pairs of elements, and when we multiply all pairs of elements, must be very close to a subfield.",

author = "Avi Wigderson",

year = "2006",

doi = "10.1109/CCC.2006.9",

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isbn = "0769525962",

series = "Proceedings of the Annual IEEE Conference on Computational Complexity",

pages = "111",

booktitle = "Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006",

note = "21st Annual IEEE Conference on Computational Complexity, CCC 2006 ; Conference date: 16-07-2006 Through 20-07-2006",

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Wigderson, A 2006, Applications of the sum-product theorem in finite fields. in Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006., 1663730, Proceedings of the Annual IEEE Conference on Computational Complexity, vol. 2006, pp. 111, 21st Annual IEEE Conference on Computational Complexity, CCC 2006, Prague, Czech Republic, 16/07/06. https://doi.org/10.1109/CCC.2006.9

Applications of the sum-product theorem in finite fields. / Wigderson, Avi.
Proceedings - Twenty-First Annual IEEE Conference on Computational Complexity, CCC 2006. 2006. p. 111 1663730 (Proceedings of the Annual IEEE Conference on Computational Complexity; Vol. 2006).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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Applications of the sum-product theorem in finite fields

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