Results 131 to 140 of about 8,990 (153)

Diophantine inequalities

1993
Abstract In order to proceed, it is necessary to show that the positive solution sets of systems of linear Diophantine equations are finitely generated. One might compare this with the famous simplex algorithm, which is well known to the practitioners of economic speculation.
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The Solubility of Certain Diophantine Inequalities

Proceedings of the London Mathematical Society, 1958
The author proves the following theorem: Let \(\lambda_1, \ldots, \lambda_{14}\) be non-zero real numbers, not all of the same sign, and suppose that \(\lambda_1/\lambda_2\) is irrational. Then, for any real \(\gamma\), and any \(\varepsilon > 0\), the inequality \[ \vert \lambda_1x_1^4 + \ldots + \lambda_{14}x_{14}^4 < \varepsilon \] has infinitely ...
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On a Diophantine Inequality with Reciprocals

Proceedings of the Steklov Institute of Mathematics, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Diophantine Inequalities for Forms

1991
A form F(λ) of degree k can be written as $$ F\left( \lambda \right) = \mathop{\sum }\limits_{{1 \leqslant {{i}_{1}}, \ldots ,{{i}_{k}} \leqslant s}} a\left( {{{i}_{1}}, \ldots ,{{i}_{k}}} \right){{\lambda }_{{{{i}_{l}}}}} \cdots {{\lambda }_{{{{i}_{k}}}}} $$ we associate the multilinear form $$ \hat F\left( \lambda \right) = \sum\limits_{1 \
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Systems of cubic Diophantine inequalities

Journal für die reine und angewandte Mathematik (Crelles Journal), 2004
The main purpose of this work is to show that whenever \(R\) and \(s\) are positive integers with \(s\geq(10R)^{(10R)^5}\), then for any given real cubic forms \(C_1({\mathbf x}), \ldots, C_R({\mathbf x})\) in \(s\) variables, there exists a vector \({\mathbf x}=(x_1,\ldots,x_s)\) with integers \(x_1,\ldots,x_s\), not all zero, satisfying \(| C_i ...
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Diophantine inequality involving binary forms

Frontiers of Mathematics in China, 2017
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Diophantine inequality involving binary forms

Frontiers of Mathematics in China, 2013
This paper is concerned with the study of Diophantine inequalities that are composed of binary forms. Let \(\phi_j\in \mathbb{Z}[x,y]\) for \(1\leq j\leq s\) be nondegenerate homogeneous forms of degree \(d=3\) or \(d=4\). Assume that \(\lambda_i\) for \(1\leq i\leq s\) are non-zero real numbers such that \(\frac{\lambda_1}{\lambda_2}\) is irrational ...
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Diophantine inequalities over Piatetski-Shapiro primes

Frontiers of Mathematics in China, 2021
Deyu Zhang
exaly  

Some Diophantine inequalities

Mathematika, 1955
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Optimality of two inequalities for exponents of Diophantine approximation

Journal of Number Theory, 2023
Johannes Schleischitz
exaly