Results 21 to 30 of about 476,689 (165)
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
Systems of quadratic diophantine inequalities [PDF]
Journal de théorie des nombres de Bordeaux, 2008 Let Q 1 , ⋯ , Q r
openaire +2 more sources
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 ...
Brüdern, Jörg, Cook, R. J.
openaire +3 more sources
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 ...
openaire +2 more sources
One Cubic Diophantine Inequality [PDF]
Journal of the London Mathematical Society, 2000 Let \(F(x)\) be a cubic form with real coefficients in \(s\) variables. \textit{J. Pitman} [J. Lond. Math. Soc. 43, 119-126 (1968; Zbl 0164.05301)] proved that there exists \(s_0> 0\) such that for any \(s\geq s_0\) the inequality \[ |F(x)|< 1 \tag{1} \] is solvable in \({\mathbf x}\in \mathbb{Z}^3\setminus \{\mathbf{0}\}\). About the quantitative part,
openaire +2 more sources
On Diophantine transference principles [PDF]
, 2018 We provide an extension of the transference results of Beresnevich and Velani connecting homogeneous and inhomogeneous Diophantine approximation on manifolds and provide bounds for inhomogeneous Diophantine exponents of affine subspaces and their ...
ANTOINE MARNAT +3 more
core +1 more source
On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
wiley +1 more source
Cubic diophantine inequalities III
Periodica Mathematica Hungarica, 1996 This paper reports on the continuing investigation by the author of the distribution of the values of diagonal cubic forms in seven and eight variables [Mathematica 35, 51-58 (1988; Zbl 0659.10015) and J. Lond. Math. Soc. (2) 53, 1-18 (1996; Zbl 0858.11018)]. The results of the present paper are as follows.
openaire +4 more sources
Symmetric modular Diophantine inequalities [PDF]
Proceedings of the American Mathematical Society, 2006 In this paper we study and characterize those Diophantine inequalities a x mod
openaire +2 more sources
On transfer inequalities in Diophantine approximation, II [PDF]
Mathematische Zeitschrift, 2009 We refine Khintchine Transference Principle which relates the measure of simultaneous rational approximation of an $n$ real numbers with the measure of linear independence of these $n$ numbers. Khintchine's inequalities are known to be optimal. However, they may be sharpened by taking into account two further uniform exponents.
Bugeaud, Yann, Laurent, Michel
openaire +3 more sources