Results 1 to 10 of about 37 (37)

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
doaj   +1 more source

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

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

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

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
doaj   +1 more source

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
doaj   +1 more source

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
doaj   +1 more source

Polynomial progressions in topological fields

Forum of Mathematics, Sigma
Let $P_1, \ldots , P_m \in \mathbb {K}[\mathrm {y}]$ be polynomials with distinct degrees, no constant terms and coefficients in a general local field $\mathbb {K}$ . We give a quantitative count of the number of polynomial progressions $
Ben Krause, Mariusz Mirek, Sarah Peluse, James Wright   +3 more
doaj   +1 more source