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(1)
Finite Field
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An Inverse Theorem for the Uniformity Seminorms Associated with the Action of
An Inverse Theorem for the Uniformity Seminorms Associated with the Action of,10.1007/s0003901000511,Vitaly Bergelson,Terence Tao,Tamar Ziegler
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An Inverse Theorem for the Uniformity Seminorms Associated with the Action of
(
Citations: 4
)
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Vitaly Bergelson
,
Terence Tao
,
Tamar Ziegler
Published in 2010.
DOI:
10.1007/s0003901000511
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Citation Context
(2)
...[TZ2], [
BTZ
]. We combine this result with some abstract arguments in order to prove that a bounded function can be expressed as a sum of polynomial phases and a part that is small in the appropriate uniformity norm...
...we shall state formally in the next section, has been proved by Bergelson, Tao and Ziegler [
BTZ
], [TZ2]...
...However, even after these examples it was reasonable to believe that the conjecture was true whenever the characteristic p was sufficiently large, and this was eventually proved by Bergelson, Tao and Ziegler [
BTZ
], [TZ2]...
W. T. Gowers
,
et al.
Linear Forms and HigherDegree Uniformity for Functions On
...Lovett et al. [4] and Green and Tao [3] disproved this conjecture as stated, but a modication of the conjecture remains open, and was recently proven in high characteristic [
9
], [10]...
Arnab Bhattacharyya
,
et al.
Optimal Testing of ReedMuller Codes
References
(18)
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Citations: 9
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Journal:
Bulletin of The London Mathematical Society  BULL LOND MATH SOC
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Distribution of values of bounded generalized polynomials
(
Citations: 13
)
Vitaly Bergelson
,
Alexander Leibman
Journal:
Acta Mathematica  ACTA MATH
, vol. 198, no. 2, pp. 155230, 2007
A new proof of Szemerédi's theorem
(
Citations: 119
)
T. Gowers
Journal:
Geometric and Functional Analysis  GEOM FUNCT ANAL
, vol. 11, no. 3, pp. 465588, 2001
Multiple recurrence and convergence for sequences related to the prime numbers
(
Citations: 13
)
Nikos Frantzikinakis
,
Bernard Host
,
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Journal:
Journal Fur Die Reine Und Angewandte Mathematik  J REINE ANGEW MATH
, vol. 2007, no. 611, pp. 131144, 2007
Ergodic behavior of diagonal measures and a theorem of Szemerédi on arithmetic progressions
(
Citations: 212
)
Harry Furstenberg
Journal:
Journal D Analyse Mathematique  J ANAL MATH
, vol. 31, no. 1, pp. 204256, 1977
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Citations
(4)
Linear Forms and HigherDegree Uniformity for Functions On
(
Citations: 4
)
W. T. Gowers
,
J. Wolf
Journal:
Geometric and Functional Analysis  GEOM FUNCT ANAL
, vol. 21, no. 1, pp. 3669, 2011
AN INVERSE THEOREM FOR THE GOWERS U4NORM
(
Citations: 59
)
BEN GREEN
,
TERENCE TAO
,
TAMAR ZIEGLER
Published in 2010.
Optimal Testing of ReedMuller Codes
(
Citations: 2
)
Arnab Bhattacharyya
,
Swastik Kopparty
,
Grant Schoenebeck
,
Madhu Sudan
,
David Zuckerman
Conference:
IEEE Symposium on Foundations of Computer Science  FOCS
, pp. 488497, 2010
Large values of the GowersHostKra seminorms
Tanja Eisner
,
Terence Tao
Published in 2010.