Results 61 to 70 of about 8,990 (153)
Diophantine approximation with one prime, two squares of primes and one $k$-th power of a prime
, 2017 Let ...
Gambini, Alessandro
core
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_ ...
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Euclidean algorithms are Gaussian over imaginary quadratic fields
Journal of the London Mathematical Society, Volume 112, Issue 6, December 2025.Abstract We prove that the distribution of the number of steps of the Euclidean algorithm of rationals in imaginary quadratic fields with denominators bounded by N$N$ is asymptotically Gaussian as N$N$ goes to infinity, extending a result by Baladi and Vallée for the real case.
Dohyeong Kim, Jungwon Lee, Seonhee Lim
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Diophantine inequalities in function fields [PDF]
Bulletin of the London Mathematical Society, 2009 This paper develops the Bentkus-Gotze-Freeman variant of the DavenportHeilbronn method for function fields in order to count Fq[t]-solutions to diagonal Diophantine inequalities in Fq((1/t)).
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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.
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Diophantine inequalities with power sums [PDF]
Journal de théorie des nombres de Bordeaux, 2008 The ring of power sums is formed by complex functions on ℕ of the formα(n)=b1c1n+b2c2n+...+bhchn,for some b i ∈ℚ ¯ and c i ∈ℤ. Let F(x,y)∈ℚ ¯[x,y] be absolutely irreducible, monic and of degree at least 2 in y. We consider Diophantine inequalities of the form|F(α(n),y)|<|∂F∂y(α(n),y)|·|α(n)|-εand show that all the solutions (n,y)∈ℕ×ℤ have y ...
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Systems of diagonal Diophantine inequalities [PDF]
Transactions of the American Mathematical Society, 2003 We treat systems of real diagonal forms F 1 ( x ) , F 2 ( x ) , … , F R ( x ) F_1(\mathbf {x}), F_2(\mathbf {x ...
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Polytool: polynomial interpretations as a basis for termination analysis of Logic programs
, 2009 Our goal is to study the feasibility of porting termination analysis techniques developed for one programming paradigm to another paradigm. In this paper, we show how to adapt termination analysis techniques based on polynomial interpretations - very ...
De Schreye, Danny +3 more
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On the x-coordinates of Pell equations that are sums of two Padovan numbers. [PDF]
Bol Soc Mat Mex, 2021 Ddamulira M.
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Analytic Methods for Diophantine Equations and Diophantine Inequalities
, 2005 Harold Davenport was one of the truly great mathematicians of the twentieth century. Based on lectures he gave at the University of Michigan in the early 1960s, this book is concerned with the use of analytic methods in the study of integer solutions to Diophantine equations and Diophantine inequalities.
H. Davenport, T. D. Browning
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