Results 1 to 10 of about 8,990 (153)

Cubic Diophantine inequalities [PDF]

Mathematika, 1982
\textit{H. Davenport} and \textit{K. F. Roth} [Mathematika, 2, 81--96 (1955; Zbl 0066.29301)] showed that for \(s \geq 8\) the values of the real additive form \(\lambda_1 x^3_1 + \ldots + \lambda_s x^3_s\) on \(\mathbb{Z}^s\) are dense on the real line, provided that \(\lambda_1/ \lambda_2\) is irrational.
Baker, R. C., Brüdern, J., Wooley, T. D.   +2 more
exaly   +8 more sources

Mersenne version of Brocard-Ramanujan equation

Journal of New Results in Science, 2023
In this study, we deal with a special form of the Brocard-Ramanujan equation, which is one of the interesting and still open problems of Diophantine analysis.
Ayşe Nalli, Seyran İbrahimov
doaj   +1 more source

A System of Two Diophantine Inequalities with Primes

Journal of Mathematics, 2021
Let ...
Xue Han, Huafeng Liu, Deyu Zhang
doaj   +1 more source

Diophantine approximation with one prime, two squares of primes and one kth power of a prime

Open Mathematics, 2021
Let ...
Gambini Alessandro
doaj   +1 more source

DIOPHANTINE INEQUALITIES OF FRACTIONAL DEGREE [PDF]

Mathematika, 2021
Accepted for publication in ...
openaire   +2 more sources

The integral part of a nonlinear form with a square, a cube and a biquadrate

Open Mathematics, 2020
In this paper, we show that if λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} are non-zero real numbers, and at least one of the numbers λ1,λ2,λ3{\lambda }_{1},{\lambda }_{2},{\lambda }_{3} is irrational, then the integer parts of λ1n12+λ2n23+λ3n34{
Ge Wenxu, Li Weiping, Zhao Feng
doaj   +1 more source

Observation of vibrating systems at different time instants

Electronic Journal of Qualitative Theory of Differential Equations, 2014
In this paper, we obtain new observability inequalities for the vibrating string. This work was motivated by a recent paper of A. Szijártó and J.
Ambroise Vest
doaj   +1 more source

A note on Diophantine inequalities in function fields [PDF]

Notes on Number Theory and Discrete Mathematics
We will discuss how the Bentkus–Götze–Freeman variant of the Davenport–Heilbronn circle method can be used to study 𝔽_q[t] solutions to inequalities of the form ord(λ₁p₁ᵏ+...+λₛpₛᵏ-γ)
Kathryn Wilson
doaj   +1 more source

Exceptional Sets for Diophantine Inequalities [PDF]

International Mathematics Research Notices, 2013
We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N^{1-c}), for a positive number c.
Parsell, Scott T., Wooley, Trevor D.
openaire   +3 more sources

Local Diophantine Nullstellen inequalities [PDF]

Journal of the American Mathematical Society, 1988
The main result of this paper is as follows. Let \(P_1,\ldots, P_n\) be polynomials of total degree at most \(D\) in \(x_1,\ldots,x_m\), with rational integer coefficients of absolute values at most \(H\).
openaire   +2 more sources