Results 1 to 10 of about 36 (36)

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

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

Lucas non-Wieferich primes in arithmetic progressions and the abc conjecture

Open Mathematics, 2023
We prove the lower bound for the number of Lucas non-Wieferich primes in arithmetic progressions. More precisely, for any given integer k≥2k\ge 2, there are ≫logx\gg \hspace{0.25em}\log x Lucas non-Wieferich primes p≤xp\le x such that p≡±1(modk)p\equiv ...
Anitha K., Fathima I. Mumtaj, Vijayalakshmi A. R.   +2 more
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

Monochromatic products and sums in the rationals

Forum of Mathematics, Pi
We show that every finite coloring of the rationals contains monochromatic sets of the form $\{x,y,xy,x+y\}$ .
Matt Bowen, Marcin Sabok
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

Distribution of Primes and Several Applications

, 2012
Petar Popivanov - This talk deals with several classical and more modern results from the theory of primes and is devoted to a larger audience. A short survey is given and almost primes of order two are discussed too.
Попиванов, Петър
core  

Large subsets of  Z m n without arithmetic progressions. [PDF]

Des Codes Cryptogr, 2023
Elsholtz C, Klahn B, Lipnik GF.
europepmc   +1 more source

COVID-19 Identification System Using Transfer Learning Technique With Mobile-NetV2 and Chest X-Ray Images. [PDF]

Front Public Health, 2022
Ragab M, Alshehri S, Azim GA, Aldawsari HM, Noor A, Alyami J, Abdel-Khalek S.   +6 more
europepmc   +1 more source

Does electrophilic activation of nitroalkanes in polyphosphoric acid involve formation of nitrile oxides? [PDF]

RSC Adv, 2021
Aksenov AV, Aksenov NA, Kirilov NK, Skomorokhov AA, Aksenov DA, Kurenkov IA, Sorokina EA, Nobi MA, Rubin M.   +8 more
europepmc   +1 more source