The ‘pits effect’ for entire functions of exponential type and the Wiener spectrum

Jacques Benatar, Alexander Borichev, Mikhail Sodin

Research output: Contribution to journalArticlepeer-review

Abstract

Given a sequence (Formula presented.), we find a simple spectral condition which guarantees the angular equidistribution of the zeroes of the Taylor series (Formula presented.) This condition yields practically all known instances of random and pseudo-random sequences (Formula presented.) with this property (due to Nassif, Littlewood, Chen–Littlewood, Levin, Eremenko–Ostrovskii, Kabluchko–Zaporozhets, Borichev–Nishry–Sodin), and provides several new ones. Among them are Besicovitch almost periodic sequences and multiplicative random sequences. It also conditionally yields that the Möbius function (Formula presented.) has this property assuming ‘the binary Chowla conjecture’.

Original languageEnglish
Pages (from-to)1433-1451
Number of pages19
JournalJournal of the London Mathematical Society
Volume104
Issue number3
DOIs
StatePublished - Oct 2021

Keywords

  • 30C15 (secondary)
  • 30D99 (primary)

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