The Distribution of Spacings Between the Fractional Parts of ndα-Reference-Cited by-同舟云学术

The Distribution of Spacings Between the Fractional Parts of ndα

Published:2021-03-31 Issue: Volume: Page:
ISSN:1073-7928
Container-title:International Mathematics Research Notices
language:en
Short-container-title:

Author:

Fassina Martino¹,Kim Sun²,Zaharescu Alexandru³

Affiliation:

1. Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria

2. Department of Mathematics, and Institute of Pure and Applied Mathematics, Jeonbuk National University, 567 Baekje-daero, Jeonju 54896, Republic of Korea

3. Department of Mathematics, University of Illinois at Urbana-Champaign 1409 West Green Street, Urbana, IL 61801, USA, and Simon Stoilow Institute of Mathematics of the Romanian Academy, P.O. Box 1-764, RO-014700 Bucharest, Romania

Abstract

Abstract We study the distribution of spacings between the fractional parts of $n^d\alpha $. For $\alpha $ of high enough Diophantine type we prove a necessary and sufficient condition for $n^d\alpha \mod 1, 1\leq n\leq N,$ to be Poissonian as $N\to \infty $ along a suitable subsequence.

Funder

National Research Foundation of Korea

Korean Government

Publisher

Oxford University Press (OUP)

Subject

General Mathematics

Link

http://academic.oup.com/imrn/advance-article-pdf/doi/10.1093/imrn/rnab022/36833833/rnab022.pdf

Reference20 articles.

1. Graduate Studies in Mathematics;Adams;An Introduction to Gröbner Bases,1994

2. Level clustering in the regular spectrum;Berry;Proc. Royal Soc. London A,1977

3. Pair correlation of values of rational functions (mod $p$);Boca;Duke Math. J.,2000

4. On exponential sums in finite fields;Bombieri;Am. J. Math.,1966

5. Statistical properties of the quasi-energy spectrum of a simple integrable system;Casati;Phys. Lett. A,1987