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On the distribution mod 1 of the sequence nα

Web1 de jan. de 1984 · Indagationes Mathematicae (Proceedings) Volume 87, Issue 3, 1984, Pages 315-327, 1984, Pages 315-327 Web1 de set. de 2003 · Let α be an irrational number and let D N*(α) and DN(α) denote the star-discrepancy and the discrepancy of the sequence (nα)n ≥1 mod 1, resp.

The Three Gap Theorem (Steinhaus Conjecture) - Cambridge Core

WebH. HEILBRONN; ON THE DISTRIBUTION OF THE SEQUENCE n2θ (mod 1), The Quarterly Journal of Mathematics, Volume os-19, Issue 1, 1 January 1948, Pages 249–256, https We use cookies to enhance your experience on our website.By continuing to use our website, you are agreeing to our use of cookies. WebJ. Surányi, Über die Anordnung der Vielfachen einer reellen Zahl mod 1,Ann. Univ. Sci. Budapest Eötvös Sect. Math. 1, (1958), 107–111. Google Scholar S. Swierczkowski , On successive settings of an arc on the circumference of a circle, Found. farming magic tree https://hartmutbecker.com

On the Distribution of nθ Modulo 1 - Cambridge Core

Web30 de jun. de 2024 · Abstract: A well known result in the theory of uniform distribution modulo one (which goes back to Fejér and Csillag) states that the fractional parts $\{n^\alpha\}$ of the sequence $(n^\alpha)_{n\ge1}$ are uniformly distributed in the unit interval whenever $\alpha>0$ is not an integer. WebProof First note that the definition of an equidistributed sequence is equivalent to the integral criterion whenever f is the indicator function of an interval: If f = 1 [c, d], then the left hand side is the proportion of points of the sequence falling in the interval [c, d], and the right hand side is exactly .. This means 2 ⇒ 1 (since indicator functions are Riemann … Web4 de jan. de 2006 · Assume that α is an irrational number with continued fraction expansion [a0;a1, . . .] and convergents ,n= 0, 1 . . . . Every positive integer N has a unique expansion N=b0q0+b1q1+ . . . +b m q m , where the digits b i are nonnegative integers with b0 farming mailers

Randomness of the square root of 2 and the Giant Leap, Part 1

Category:An Explicit Formula for the L2-Discrepancy of (nα)-Sequences

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On the distribution mod 1 of the sequence nα

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Web20 de nov. de 2024 · On the Distribution of the Sequence n2θ (mod 1) - Volume 39 Issue 2 Skip to main content Accessibility help We use cookies to distinguish you from other … Web23 de mar. de 2024 · Halton J H 1965 The distribution of the sequence {nξ}(n=0,1,2,⋯) Proc. Camb. Phil. Soc. 61 665–70. ... Sós V T 1958 On the distribution mod 1 of the …

On the distribution mod 1 of the sequence nα

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Web2 de out. de 2024 · Summary: The Three Gap Theorem, also known as the Steinhaus Conjecture, is a classical result on the combinatorics of the fractional part function, and has since been generalized in many ways. WebWe say the sequence {ξj} is Poisson distributed if lim N→∞ EN(k,L) = Lk k! e−L This means {ξj} behaves like a generic realization of independent random vari-ables mod 1. …

WebH. HEILBRONN, ON THE DISTRIBUTION OF THE SEQUENCE n 2 θ (mod 1), The Quarterly Journal of Mathematics, Volume os-19, Issue 1, 1948, Pages 249–256, … Webadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A

WebWe say the sequence {ξj} is Poisson distributed if lim N→∞ EN(k,L) = Lk k! e−L This means {ξj} behaves like a generic realization of independent random vari-ables mod 1. … Web24 de out. de 2008 · Gaps and steps for the sequence nθ mod 1 - Volume 63 Issue 4. Skip to main content Accessibility help We use cookies to distinguish you from other users …

Web18 de jun. de 2024 · Title: On the Uniform Distribution (mod 1) of the Farey Sequence, quadratic Farey and Riemann sums with a remark on local integrals of $ζ(s)$ Authors: Michel Weber Download PDF

Web30 de jun. de 2024 · Abstract: A well known result in the theory of uniform distribution modulo one (which goes back to Fejér and Csillag) states that the fractional parts … farming mag warframeWeb31 de mar. de 2024 · Fix $\alpha,\theta >0$, and consider the sequence $(\alpha n^{\theta} \mod 1)_{n\ge 1}$. Since the seminal work of Rudnick--Sarnak (1998), and due to the Berry--Tabor conjecture in quantum chaos ... free printable word search 6th gradeWebof Koksma-Erdos-Tura´n which bounds the discrepancy of a sequence by a weighted sum of the values of its Weyl sums. In the joint paper “Berry-Esseen bounds and a theorem of Erd˝os and Tura´n on uniform distribution mod 1” [29] with Walter Philipp - this paper appeared in the Duke Mathematical Journal in 1973 - a much more general result ... free printable word searches carsWebUniform distribution mod 1 and a set of full Lebesgue measure Part of the proof that Voronin gave for Theorem 1 and that we will simi- ... For rational α, the sequence (⌊nα⌋θ)n∈N is u.d. mod 1 either for all irrationals θ or for no real number θ, depending on whether α 6= 0 or α = 0. If α is irrational, ... farming management internshipsWeb9 de abr. de 2009 · This paper is concerned with the distribution of N points placed consecutively around the circle by an angle of α. We offer a new proof of the Steinhaus … free printable word searches for decemberWebof distribution of a sequence xn mod 1, n = 1;2;:::, with the set G(xn mod 1) of all distribution functions (abbreviating d.f.s) of the sequence xn mod 1, 2000 Mathematics … free printable word search bookletWebIn this paper we investigate powers of prefixes of Sturmian sequences. We give an explicit formula for ice(ω), the initial critical exponent of a Sturmian sequence ω, defined as the … farming management n5 subjects