Poisson statistics via the Chinese Remainder Theorem
2008 (English)In: Advances in Mathematics, ISSN 0001-8708, E-ISSN 1090-2082, Vol. 218, no 6, 2013-2042 p.Article in journal (Refereed) Published
We consider the distribution of spacings between consecutive elements in subsets of Z/qZ, where q is highly composite and the subsets are defined via the Chinese Remainder Theorem. We give a sufficient criterion for the spacing distribution to be Poissonian as the number of prime factors of q tends to infinity, and as an application we show that the value set of a generic polynomial modulo q has Poisson spacings. We also study the spacings of subsets of Z/q(1)q(2)Z that are created via the Chinese Remainder Theorem from subsets of Z/q(1)Z and Z/q(2)Z (for q(1), q(2) coprime), and give criteria for when the spacings modulo q(1)q(2) are Poisson. Moreover, we also give some examples when the spacings modulo q(1)q(2) are not Poisson, even though the spacings modulo q(1) and modulo q(2) are both Poisson.
Place, publisher, year, edition, pages
2008. Vol. 218, no 6, 2013-2042 p.
poisson spacings, correlation functions, distribution modulo one, quadratic residues, spacings
IdentifiersURN: urn:nbn:se:kth:diva-17709DOI: 10.1016/j.aim.2008.04.001ISI: 000257807400010ScopusID: 2-s2.0-46049102767OAI: oai:DiVA.org:kth-17709DiVA: diva2:335754
QC 201005252010-08-052010-08-05Bibliographically approved