On the orbits of multiplicative pairs

• We characterize all pairs of completely multiplicative functions fg : N -> T, where T denotes the unit circle, such that <({f(n), g(n+1))}(n >= 1))over bar> not equal T x T. In so doing, we settle an old conjecture of Zoltan Daroczy and Imre Katai.

Subject headings

NATURVETENSKAP  -- Matematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics (hsv//eng)

Keyword

multiplicative functions

Erdos discrepancy problem

Katai conjecture

Publication and Content Type

ref (subject category)

art (subject category)