On localization of the zeroes Hermite–Padé approximants to the exponential functions

The upper estimates are determined for modules of the zeros of Hermite polynomials (Hermite–Padé approximation type I) of the exponential system $\{e^{\lambda_pz}\}_{p=0}^k$, where $\{\lambda_p\}_{p=0}^k$ are arbitrary complex numbers. The proven statements complement and gen- eralize known results about the behavior of the zeros of Hermite polynomials for exponential system $\{e^{pz}\}_{p=0}^k$ by E. Saff and R. Varga, H. Stahl, F. Wielonsky.