Results 11 to 20 of about 304 (165)
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.
Brüdern, Jörg
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Exceptional Sets for Diophantine Inequalities [PDF]
International Mathematics Research Notices, 2013 We apply Freeman's variant of the Davenport-Heilbronn method to investigate the exceptional set of real numbers not close to some value of a given real diagonal form at an integral argument. Under appropriate conditions, we show that the exceptional set in the interval [-N,N] has measure O(N^{1-c}), for a positive number c.
Parsell, Scott T., Wooley, Trevor D.
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Systems of quadratic diophantine inequalities [PDF]
Journal de théorie des nombres de Bordeaux, 2008 Let Q 1 , ⋯ , Q r
Wolfgang Müller, Müller, Wolfgang
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An improved estimate for certain Diophantine inequalities [PDF]
Proceedings of the American Mathematical Society, 1980 Let λ 1
Liu, M.C., Ng, Shu Ming, Tsang, K.M.
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Old and new conjectured diophantine inequalities [PDF]
Bulletin of the American Mathematical Society, 1990 This paper is a general survey of certain Diophantine conjectures of current interest, and relations between them. In this case, the discussion revolves around the Szpiro conjecture relating the modular height and conductor of elliptic curves defined over a fixed number field. The author shows that this is equivalent to the ``\(abc\)'' conjecture (if \(
Serge Lang
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Gowers norms control diophantine inequalities [PDF]
Algebra & Number Theory, 2017 A central tool in the study of systems of linear equations with integer coefficients is the Generalised von Neumann Theorem of Green and Tao. This theorem reduces the task of counting the weighted solutions of these equations to that of counting the weighted solutions for a particular family of forms, the Gowers norms $\Vert f \Vert_{U^{s+1}[N]}$ of ...
Aled Walker
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Diophantine inequalities with mixed powers, II
Journal of Number Theory, 1979 AbstractIt is shown that if λ1, …, λ5 are non-zero real numbers, not all of the same sign, and at least one of the ratios λiλj (1 ≤ j ≤ 3) is irrational then the values taken by λ1x12 + λ2x22 + λ3x32 + λ4x43 + λ5x53 for integer values of x1, …, x5 are everywhere dense on the real line.
Harman, G, Baker, R.C
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Additive Diophantine inequalities with mixed powers II
Mathematika, 1987 Let \(1\leq k_ 1\leq k_ 2...\leq k_ s\) be integers. The author considers the following, so-called inequality problem for \(k_ 1,...,k_ s:\) is it true, that for every s-tuple of non-zero real numbers \((\lambda_ 1,...,\lambda_ s)\) such that at least one quotient \(\lambda_ i/\lambda_ j\) is irrational, the values assumed by \(\sum^{s}_{i=1}\lambda_ ...
Brüdern, Jörg
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Diophantine approximation with one prime, two squares of primes and one kth power of a prime
Open Mathematics, 2021 Let ...
Gambini Alessandro
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