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’.
- 30C15 (secondary)
- 30D99 (primary)