Results 1 to 10 of about 280 (40)
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
doaj +1 more source
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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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
doaj +1 more source
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
wiley +1 more source
Ultimate parameters of the photon collider at the ILC [PDF]
, 2006 At linear colliders, the e+e- luminosity is limited by beam-collision effects, which determine the required emittances of beams in damping rings (DRs).
A. V. Pak +16 more
core +2 more sources
Towers for commuting endomorphisms, and combinatorial applications [PDF]
, 2016 We give an elementary proof of a generalization of Rokhlin's lemma for commuting non-invertible measure-preserving transformations, and we present several combinatorial applications.Comment: 13 pages. Referee's comments incorporated. To appear in Annales
Avila, Artur, Candela, Pablo
core +3 more sources
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
doaj +1 more source
, 2015 Given a definably amenable approximate subgroup $A$ of a (local) group in some first-order structure, there is a type-definable subgroup $H$ normalised by $A$ and contained in $A^4$ such that every definable superset of $H$ has positive ...
Massicot, Jean-Cyrille +1 more
core +5 more sources
A low-energy decomposition theorem [PDF]
, 2015 We prove that any finite set of real numbers can be split into two parts, one part being highly non-additive and the other highly non-multiplicative.Comment: 16 ...
Balog, Antal, Wooley, Trevor D.
core +3 more sources
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
doaj +1 more source