The Malliavin – Rubel theorem on entire functions of exponential type with given zeros: 60 years later

For distributions of points $Z$ and $W$ on the positive semiaxis, the Malliavin – Rubel theorem of 1961 establishes necessary and sufficient conditions under which for an entire function of exponential type $g\neq 0$ with $g(W)=0$ there is an entire function of exponential type $f\neq 0$ with $f(Z)=0$, such that $|f|\leq |g|$ on the imaginary axis. In the talk we discuss the development of this theorem for arbitrary $Z$ and $W$ on the complex plane, as well as its subharmonic versions and close connection with the famous Beurling – Malliavin theorems on the radius of completeness and the multiplier.