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A System of Two Diophantine Inequalities with Primes [PDF]
Journal of Mathematics, 2021 Let ...
Xue Han, Huafeng Liu, Deyu Zhang
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Cubic Diophantine inequalities [PDF]
Mathematika, 1995 \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.
J Brüdern, T D Wooley
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Cubic Diophantine inequalities [PDF]
Mathematika, 1982 Let \(\lambda_1,\ldots,\lambda_s\) be non-zero real numbers and not all ratios \(\lambda_i/\lambda_j\) be rational. \textit{H. Davenport} and \textit{K. F. Roth} [Mathematika 2, 81--96 (1955; Zbl 0066.29301)] proved that the values taken by \(\lambda_1x^3_1+\cdots+\lambda_8x^3_8\) at integer points \(x_1,\ldots,x_8\), are dense on the real line. Later,
Brüdern, Jörg
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Quadratic Diophantine Inequalities
Journal of Number Theory, 2001 The theme of this paper is to investigate certain systems of Diophantine inequalities on real diagonal quadratic forms. First, let \(Q_1\) and \(Q_2\) be real diagonal quadratic forms in \(s\) variables, with \(s\geq 10\), and suppose that whenever \(\alpha\) and \(\beta\) are real numbers with \((\alpha,\beta)\neq(0,0)\), then the form \(\alpha Q_1 ...
Freeman, D.Eric
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Diophantine Inequalities for Polynomial Rings
Journal of Number Theory, 1999 The author studies the Hardy-Littlewood method for the Laurent series field \(\mathbb F_q ((1/T))\) over the finite field \(\mathbb F_q\) with \(q\) elements. He shows that if \(\lambda_1\), \(\lambda_2\), \(\lambda_3\) are nonzero elements in \(\mathbb F_q ((1/T))\) satisfying \(\lambda_1/\lambda_2\not\in \mathbb F_q(T)\) and \(\text{sgn} (\lambda_1)+
Chih-Nung Hsu
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Proportionally modular diophantine inequalities
Journal of Number Theory, 2003 The authors study the sets of nonnegative solutions of Diophantine inequalities of the form \(ax\) mod \(b \leq cx\) with \(a, b\) and \(c\) positive integers. These sets are numerical semigroups, which are investigated and characterized.
J C Rosales
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On pairs of cubic Diophantine inequalities
Mathematika, 1991 \textit{H. Davenport} and \textit{H. Heilbronn} [J. Lond. Math. Soc. 21, 185--193 (1946; Zbl 0060.11914)] proved that if \(Q({\mathbf x})=\sum^5_{j=1}\lambda_jx^2_j\) is an indefinite quadratic form with real coefficients \(\lambda_j\), such that at least one of the ratios \(\lambda_i/\lambda_j\) is irrational, then for any \(\varepsilon>0\) there ...
J Brüdern
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On two Diophantine inequalities over primes [PDF]
Indagationes Mathematicae, 2018 21 ...
Min Zhang, Jinjiang Li
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Cubic diophantine inequalities for split forms [PDF]
Monatshefte Fur Mathematik, 2014 Denote by $s_0^{(r)}$ the least integer such that if $s \ge s_0^{(r)}$, and $F$ is a cubic form with real coefficients in $s$ variables that splits into $r$ parts, then $F$ takes arbitrarily small values at nonzero integral points. We bound $s_0^{(r)}$ for $r \le 6$.
Sam Chow
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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
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