Asymptotics of the Zeros of Degenerate Hypergeometric Functions

We find the asymptotics of the zeros of the degenerate hypergeometric function (the Kummer function) $\Phi(a,c;z)$ and indicate a method for numbering all of its zeros consistent with the asymptotics. This is done for the whole class of parameters $a$ and $c$ such that the set of zeros is infinite. As a corollary, we obtain the class of sine-type functions with unfamiliar asymptotics of their zeros. Also we prove a number of nonasymptotic properties of the zeros of the function $\Phi$.