Skip to content

Pair correlation for quadratic polynomials mod 1

Research output: Contribution to journalArticle

Original languageEnglish
Pages (from-to)960-983
Number of pages24
JournalCompositio Mathematica
Volume154
Issue number5
Early online date20 Mar 2018
DOIs
DateAccepted/In press - 10 Nov 2017
DateE-pub ahead of print - 20 Mar 2018
DatePublished (current) - May 2018

Abstract

It is an open question whether the fractional parts of nonlinear polynomials at integers have the same fine-scale statistics as a Poisson point process. Most results towards an affirmative answer have so far been restricted to almost sure convergence in the space of polynomials of a given degree. We will here provide explicit Diophantine conditions on the coefficients of polynomials of degree 2, under which the convergence of an averaged pair correlation density can be established. The limit is consistent with the Poisson distribution. Since quadratic polynomials at integers represent the energy levels of a class of integrable quantum systems, our findings provide further evidence for the Berry-Tabor conjecture in the theory of quantum chaos.

Download statistics

No data available

Documents

Documents

  • Full-text PDF (accepted author manuscript)

    Rights statement: This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Cambridge University Press at https://www.cambridge.org/core/journals/compositio-mathematica/article/pair-correlation-for-quadratic-polynomials-mod-1/8EBB2BCAF26312E3B4E15E7DD2701C0F . Please refer to any applicable terms of use of the publisher.

    Accepted author manuscript, 576 KB, PDF document

DOI

View research connections

Related faculties, schools or groups