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 users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings. Web1 de mar. de 2024 · Given any rational number 0 < x < 1 (say, x = 1/2) and any positive integer n, we count the number of elements of the sequence α, 2α, 3α, …, nα modulo 1 that fall into the subinterval [0, x].

On the Distribution Modulo 1 of the Sequence αn2 + βn

WebUniform 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, ... 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 … highland audio aingel3201

A note on the distribution of the sequence (nα) with …

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 … Web24 de out. de 2008 · We shall describe how, for successive integers N, the points {n ξ}, with n = 0, 1, …, N – 1, are distributed in the closed unit interval U = [0, 1]; by showing how … 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. highland audio aingel

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

Local Discrepancies in the Problem of the Distribution of the Sequence ...

WebAssume that α is an irrational number with continued fraction expansion [a0;a1, . . .] and convergents **,n= 0, 1 . . . . Every positive integer N has a unique ... 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 … highland atv park in cedartown georgia highland auburn ny

"Webof 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 ... " - On the distribution mod 1 of the sequence nα

On the distribution mod 1 of the sequence nα

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

Web1 de ago. de 2011 · Let ω:= (xn)n⩾1 be any sequence of real numbers in the interval [0,1), N a positive integer and x∈ [0,1). Then DN (ω,x):=∑n=1Nc [0,x) (xn)−Nx is called the local discrepancy of the ... Web20 de nov. de 2024 · 1. Dym, H., On the structure and the Hausdorff dimension of the support of a class of distribution functions induced by ergodic sequences, Mitre Corp., T.M.-4155 (1965). 10.21236/AD0623616 CrossRef Google Scholar

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Web2 UNIFORM DISTRIBUTION MOD 1 Thus, in simple terms, the sequence is u.d. mod 1 if every half-open subinterval of I eventually gets its "proper share" of fractional parts. In the course of developing the theory of uniform distribution modulo 1 (abbreviated u.d. mod 1), we shall encounter many examples of sequences WebThe ﬁrst part is concerned with sequences of the type x k = n kα, n1 < n2 < n3 < ···, mod 1. Improving a result of ˇSala´t we show that, if the quotients q k = n k+1/n k satisfy q k ≥ 1 + ε, then the set of α such that (x k) is uniformly distributed is of ﬁrst Baire category, i.e. for generic α we do not have uniform distribution.

Web9 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 … 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 …

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. WebIn 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 …

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 …

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. how is bachelor of arts abbreviatedWebWe 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. … highland audi hawcoWebOn the Distribution Modulo 1 of the Sequence αn2 + βn - Volume 29 Issue 4. Skip to main content Accessibility help We use cookies to distinguish you from other users and to … how is backblaze so cheapWeb1 de jul. de 1997 · These sums are closely related to the discrepancy of the sequence ({nα}); ... On a conjecture of Erdős and Szüsz related to uniform distribution mod 1. Acta. ... Uniform Distribution of Sequences, Wiley, New York (1974) Google Scholar. 12. M. Lerch. Question 1547. l'intermédiate des Mathématiciens, 11 (1904), pp. 145-146. View ... highland audio aingel 3205 testWebof 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 … highland austin bedWeb2. Density and uniform distribution mod 1. Throughout, [x]means the great- est integer less than or equal to x; (x) = x -[x]is the fractional part of x. In discussing the uniform distribution of sequences mod 1, the notation of Kuipers and Niederreiter (1974) will be followed. Let the left-most digit of a real number how is bachata different from salsaWebH. 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, … highland audio aingel 3203