Results 21 to 30 of about 8,990 (153)
Systems of quadratic diophantine inequalities [PDF]
Journal de théorie des nombres de Bordeaux, 2008 Let Q 1 ,⋯,Q r be quadratic forms with real coefficients. We prove that for any ϵ>0 the system of inequalities |Q 1 (x)|<ϵ,⋯,|Q r (x)|<ϵ has a nonzero integer solution, provided that the system Q 1 (x)=0,⋯,Q r (x)=0 has a nonsingular real solution and all forms in the real pencil generated by Q 1 ,⋯,Q r are irrational and have rank >8r.
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Distribution of Values of Quadratic Forms at Integral Points
, 2019 The number of lattice points in $d$-dimensional hyperbolic or elliptic shells $\{m ...
Buterus, Paul +3 more
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Diophantine Inequalities as a Problem of Difference between Consecutive Primes [PDF]
, 2014 In the present paper, we have developed a method for solving \textit{diophantine inequalities} using their relationship with the \textit{difference between consecutive primes}.
Sidokhine, Felix
core
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.
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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 \(
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Moderate Deviation Principles for Lacunary Trigonometric Sums
Mathematische Nachrichten, Volume 299, Issue 5, Page 1028-1044, May 2026.ABSTRACT Classical works of Kac, Salem, and Zygmund, and Erdős and Gál have shown that lacunary trigonometric sums despite their dependency structure behave in various ways like sums of independent and identically distributed random variables. For instance, they satisfy a central limit theorem (CLT) and a law of the iterated logarithm.
Joscha Prochno, Marta Strzelecka
wiley +1 more source
On Hilbert's Tenth Problem [PDF]
, 2014 Using an iterated Horner schema for evaluation of diophantine polynomials, we define a partial $\mu$-recursive "decision" algorithm decis as a "race" for a first nullstelle versus a first (internal) proof of non-nullity for such a polynomial -- within a ...
Pfender, Michael
core
Successive Minima and Best Simultaneous Diophantine Approximations
, 2005 We study the problem of best approximations of a vector $\alpha\in{\mathbb R}^n$ by rational vectors of a lattice $\Lambda\subset {\mathbb R}^n$ whose common denominator is bounded.
Aliev, Iskander, Henk, Martin
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On the exceptional set in Littlewood's discrete conjecture
Bulletin of the London Mathematical Society, Volume 58, Issue 5, May 2026.Abstract We consider a discrete analogue of the well‐known Littlewood conjecture on Diophantine approximations and obtain a strong upper bound for the number of exceptional vectors in this conjecture.
I. D. Shkredov
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Report on some recent advances in Diophantine approximation [PDF]
, 2009 A basic question of Diophantine approximation, which is the first issue we discuss, is to investigate the rational approximations to a single real number. Next, we consider the algebraic or polynomial approximations to a single complex number, as well as
Waldschmidt, Michel
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