Results 131 to 140 of about 12,497 (156)

Asymptotic lower bounds for Diophantine inequalities

Mathematika, 2000
Let \(F({\mathbf x})=\lambda_1 x_1^k+ \cdots +\lambda_s x_s^k\) be a diagonal form with non-zero real coefficients, whose ratios are not all rational, and such that, if \(k\) is even, then not all coefficients have the same sign. In this paper the author proves that there is an absolute real positive constant \(C\), such that for every \(\epsilon >0 ...
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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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A ternary Diophantine inequality with prime numbers of a special form

Periodica Mathematica Hungarica, 2021
Jinjiang Li, Fei Xue, Min Zhang
exaly  

Some Diophantine inequalities

Mathematika, 1955
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A ternary Diophantine inequality by primes with one of the form $$p=x^2+y^2+1$$

Ramanujan Journal, 2022
exaly  

On a ternary Diophantine inequality over primes

Ramanujan Journal, 2022
exaly  

A quinary diophantine inequality by primes with one of the form $$\varvec{p=x^2+y^2+1}$$

Indian Journal of Pure and Applied Mathematics, 2022
exaly