Results 1 to 10 of about 49 (46)
High-entropy dual functions over finite fields and locally decodable codes
Forum of Mathematics, Sigma, 2021 We show that for infinitely many primes p there exist dual functions of order k over ${\mathbb{F}}_p^n$ that cannot be approximated in $L_\infty $-distance by polynomial phase functions of degree $k-1$. This answers in the negative a natural finite-field
Jop Briët, Farrokh Labib
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New lower bounds for van der Waerden numbers
Forum of Mathematics, Pi, 2022 We show that there is a red-blue colouring of $[N]$ with no blue 3-term arithmetic progression and no red arithmetic progression of length $e^{C(\log N)^{3/4}(\log \log N)^{1/4}}$.
Ben Green
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A correspondence principle for the Gowers norms [PDF]
Journal of Logic and Analysis, 2009 The Furstenberg Correspondence shows that certain "local behavior" of dynamical system is equivalent to the behavior of sufficiently large finite systems. The Gowers uniformity norms, however, are not local in the relevant sense.
H. Towsner
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Bounds for sets with no polynomial progressions
Forum of Mathematics, Pi, 2020 Let $P_1,\dots ,P_m\in \mathbb{Z} [y]$ be polynomials with distinct degrees, each having zero constant term. We show that any subset A of $\{1,\dots ,N\}$ with no nontrivial progressions of the form $x,x+P_1(y),\dots ,x+P_m(y)$ has size $|A|\ll N/(\log ...
Sarah Peluse
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Linear correlations of multiplicative functions
Proceedings of the London Mathematical Society, Volume 121, Issue 2, Page 372-425, August 2020., 2020 Abstract We prove a Green–Tao type theorem for multiplicative functions.
Lilian Matthiesen
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MIXING FOR PROGRESSIONS IN NONABELIAN GROUPS
Forum of Mathematics, Sigma, 2013 We study the mixing properties of progressions $(x, xg, x{g}^{2} )$ , $(x, xg, x{g}^{2} , x{g}^
TERENCE TAO
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POLYNOMIAL PATTERNS IN THE PRIMES
Forum of Mathematics, Pi, 2018 Let $P_{1},\ldots ,P_{k}:\mathbb{Z}\rightarrow \mathbb{Z}$ be polynomials of degree at most ...
TERENCE TAO, TAMAR ZIEGLER
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A DISTRIBUTION ON TRIPLES WITH MAXIMUM ENTROPY MARGINAL
Forum of Mathematics, Sigma, 2019 We construct an $S_{3}$-symmetric probability distribution on $\{(a,b,c)\in \mathbb{Z}_{{\geqslant}0}^{3}\,:\,a+b+c=n\}$ such that its marginal achieves the maximum entropy among all probability distributions on $\{0,1,\ldots ,n\}$ with mean $n/3 ...
SERGEY NORIN
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ROTH’S THEOREM FOR FOUR VARIABLES AND ADDITIVE STRUCTURES IN SUMS OF SPARSE SETS
Forum of Mathematics, Sigma, 2016 We show that if $A\subset \{1,\ldots ,N\}$ does not contain any nontrivial solutions to the equation
TOMASZ SCHOEN, OLOF SISASK
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UPPER BOUNDS FOR SUNFLOWER-FREE SETS
Forum of Mathematics, Sigma, 2017 A collection of $k$ sets is said to form a $k$ -sunflower ...
ERIC NASLUND, WILL SAWIN
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