Results 31 to 40 of about 12,497 (156)
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 ...
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, 2009 A Diophantine $m$-tuple is a set $A$ of $m$ positive integers such that $ab+1$ is a perfect square for every pair $a,b$ of distinct elements of $A$. We derive an asymptotic formula for the number of Diophantine quadruples whose elements are bounded by $x$
Martin, Greg, Sitar, Scott
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, 2007 We prove that a $C^{2+\alpha}$-smooth orientation-preserving circle diffeomorphism with rotation number in Diophantine class $D_\delta ...
A. Teplinsky +15 more
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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 ...
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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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A Diophantine Inequality Involving Mixed Powers of Primes with a Specific Type
MathematicsLet λ1,λ2,λ3 be nonzero real numbers, not all of the same sign; let λ1/λ2 be irrational; and let η be any real number. We investigate the solvability of the inequality |λ1p1+λ2p2+λ3p32+η|0 in the prime variables p1, p2, and p3.
Tatiana L. Todorova, Atanaska Georgieva
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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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Energy Science &Engineering, EarlyView.This study introduces bipolar q‐fractional fuzzy sets and new aggregation operators to support renewable energy selection under uncertainty. The proposed decision‐making framework effectively integrates positive and negative evaluations, ensuring consistent ranking and robust performance, as demonstrated through practical analysis and comparative ...
Sagvan Y. Musa +3 more
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