On the Behavior of Power Series with Completely Additive Coefficients
Oleg Petrushov (2015)
Bulletin of the Polish Academy of Sciences. Mathematics
Similarity:
Consider the power series , where α(n) is a completely additive function satisfying the condition α(p) = o(lnp) for prime numbers p. Denote by e(l/q) the root of unity . We give effective omega-estimates for when r → 1-. From them we deduce that if such a series has non-singular points on the unit circle, then it is a zero function.