On the behavior close to the unit circle of the power series whose coefficients are squared Möbius function values

Abstract

We consider the behavior of the power series $\mathfrak{M}_0(z)=\sum_{n=1}^{\infty}\mu^2(n)z^n$ as $z$ tends to $e(\beta)=e^{2\pi i\beta}$ along a radius of the unit circle. If $\beta$ is irrational with irrationality exponent 2 then $\mathfrak{M}_0(e(\be