On the distribution mod 1 of the sequence nα
Web1 de ago. de 2007 · On the distribution mod 1 of the sequence nα. Annals of the University of Science, Budapest Eötvös. Sect Math, I: 127 – 134. [Google Scholar] Clough, J. 1989. Review of David Lewin's Generalized Musical Intervals and Transformations. Music Theory Spectrum, 11: 226 – 231. [Google Scholar] Lewin, D. 1987. WebLet a be a real number, N a positive integer and N a subset of {0, 1, 2,..., N}. We give an upper bound for the number of distinct lengths of gaps between the fractional parts {nα}, …
On the distribution mod 1 of the sequence nα
Did you know?
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 Web4 de jan. de 2006 · be the L 2-discrepancy of the sequence (nα) mod 1, where {y} denotes the fractional part of the real number y. In this paper, we give an explicit formula for D * …
Web31 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 ... 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
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. 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. …
WebA well known result in the theory of uniform distribution modulo 1 (which goes back to Fejér and Csillag) states that the fractional ... the k k k-level correlation functions of the sequence ({n ... On the correlations of n α n^\alpha n α mod 1. J. Eur. Math. Soc. (2024), DOI 10.4171/JEMS/1281. Publication Date. 5 October 2024. Identifiers ...
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. rbac trenton business assistance corporationWebarXiv:1910.11766v1 [math.NT] 25 Oct 2024 On the discrepancyof randomsubsequences of {nα} Istva´n Berkes∗ and Bence Borda† Abstract For irrational α, {nα} is uniformly dist rbac twgWebAbstract. Let α be an irrational number and let D N * (α) and D N (α) denote the star-discrepancy and the discrepancy of the sequence (nα) n ≥1 mod 1, resp. We study … rbac testsWebH. 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, … rbac userWebIt was shown that for any sequence (an)n≥1 of distinct positive integers, the sequence (xan)n≥1 is completely uniformly distributed modulo one for almost all real numbers x with x > 1. In the paper “Metric theorems on uniform distribution and approximation theory” [38], again in cooperation with Tichy, this result was even general- rbac triangle of powerWebof 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 ... rba current interest ratesWebadshelp[at]cfa.harvard.edu The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86A rbac-tool