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On a ternary Diophantine inequality
The Ramanujan Journal, 2016zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Diophantine Inequalities for Forms
1991A 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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Diophantine inequality by unlike powers of primes
The Ramanujan Journal, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Some Nonlinear Diophantine Inequalities with Primes
Mathematical Notes, 2019\textit{S. A. Gritsenko} and \textit{Nguen Tkhi Cha} [Nauchn. Vedomosti BelGU Ser. Mat. Fiz. 23 (29), 202 (2012)] showed that if \(H\geq \sqrt{N}\exp(\ln^{-0.1}N)\), then the inequality \[ |p_1^2+p_2^2-H|\le H \] is solvable in primes \(p_1,p_2\). As in improvement, in the present paper the author shows, that if \(H\geq N^{31/64+\varepsilon}\), then ...
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Asymptotic lower bounds for Diophantine inequalities
Mathematika, 2000Let \(F({\mathbf x})=\lambda_1 x_1^k+ \cdots +\lambda_s x_s^k\) 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 binary Diophantine inequality involving prime numbers
Ramanujan Journal, 2020Yingchun Cai
exaly
A quaternary Diophantine inequality with prime numbers of a special form
Ramanujan Journal, 2023Jinjiang Li
exaly
A ternary Diophantine inequality by primes with one of the form $$p=x^2+y^2+1$$
Ramanujan Journal, 2022exaly