On series of dilated functions

István Berkes, Michel Weber*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


Given a periodic function f , we study the almost everywhere and norm convergence of series∑∞ k=1 c k f (kx). As the classical theory shows, the behavior of such series is determined by a combination of analytic and number theoretic factors, but precise results exist only in a few special cases. In this paper, we use connections with orthogonal function theory and greatest common divisor sums to prove several new results and improve old ones, and also to simplify and unify the theory.
Original languageEnglish
Pages (from-to)25-52
JournalThe Quarterly Journal of Mathematics
Issue number1
Publication statusPublished - 2014

Fields of Expertise

  • Information, Communication & Computing

Treatment code (Nähere Zuordnung)

  • Basic - Fundamental (Grundlagenforschung)


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