Results 61 to 70 of about 22,960 (196)

Irreducibility of Polynomials over Global Fields is Diophantine

, 2017
Given a global field $K$ and a positive integer $n$, we present a diophantine criterion for a polynomial in one variable of degree $n$ over $K$ not to have any root in $K$.
Dittmann, Philip
core   +1 more source

Moderate Deviation Principles for Lacunary Trigonometric Sums

Mathematische Nachrichten, Volume 299, Issue 5, Page 1028-1044, May 2026.
ABSTRACT Classical works of Kac, Salem, and Zygmund, and Erdős and Gál have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random variables. For instance, they satisfy a central limit theorem (CLT) and a law of the iterated logarithm.
Joscha Prochno, Marta Strzelecka
wiley   +1 more source

A note on the ternary Diophantine equation x2 − y2m = zn

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
Let ℕ be the set of all positive integers. In this paper, using some known results on various types of Diophantine equations, we solve a couple of special cases of the ternary equation x2 − y2m = zn, x, y, z, m, n ∈ ℕ, gcd(x, y) = 1, m ≥ 2, n ≥ 3.
Bérczes Attila, Le Maohua, Pink István, Soydan Gökhan   +3 more
doaj   +1 more source

On the exceptional set in Littlewood's discrete conjecture

Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.
Abstract We consider a discrete analogue of the well‐known Littlewood conjecture on Diophantine approximations and obtain a strong upper bound for the number of exceptional vectors in this conjecture.
I. D. Shkredov
wiley   +1 more source

Revolutionizing teaching effectiveness: integrating physical education pedagogies with smart decision making [PDF]

PeerJ Computer Science
Physical education is the method of teaching that focuses on student development through a wide range of teaching skills related to physical fitness, along with lifelong habits of health and fitness.
Bo Qi, Li Liang, Binghan Qiao
doaj   +2 more sources

An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems

Mathematics, 2023
The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research.
Salma Iqbal, Naveed Yaqoob, Muhammad Gulistan   +2 more
doaj   +1 more source

A hypothetical upper bound for the solutions of a Diophantine equation with a finite number of solutions

, 2013
We conjecture that if a system S \subseteq {x_i=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}} has only finitely many solutions in integers x_1,...,x_n, then each such solution (x_1,...,x_n) satisfies |x_1|,...,|x_n| \leq 2^{2^{n-1}}.
Tyszka, Apoloniusz
core   +1 more source

Primitive prime divisors in the critical orbit of z^d+c [PDF]

, 2012
We prove the finiteness of the Zsigmondy set associated to the critical orbit of f(z) = z^d+c for rational values of c by finding an effective bound on the size of the set.
Krieger, Holly
core   +1 more source

Sums of three positive cubes

Journal of the London Mathematical Society, Volume 113, Issue 5, May 2026.
Abstract We survey ideas surrounding the study of the number of integers that can be represented as the sum of three positive cubes. We focus on the early contribution of Davenport using elementary techniques, and the subsequent developments due to Vaughan, which introduced Fourier analysis and mirrored many of the important developments of the Hardy ...
James Maynard
wiley   +1 more source

Simultaneous diophantine approximation and IP-sets [PDF]

Acta Arithmetica, 1988
A sequence \(p_1, p_2,\ldots\) in \(\mathbb{Z}\) together with all sums \(p_{i_1}+\cdots +p_{i_k ...
Furstenberg, H., Weiss, B.
openaire   +2 more sources