Upper Bounds for the Moduli of Zeros of Hermite–Padé Approximations for a Set of Exponential Functions

In this paper, we establish upper bounds for the moduli of zeros of Hermite–Padé approximations of type I for a system of exponential functions $\{e^{\lambda_pz}\}_{p=0}^k$, where $\{\lambda_p\}_{p=0}^k$ are various arbitrary complex numbers. The proved statements supplement and generalize well-known results due to Saff and Varga, as well as those due to Stahl and Wielonsky, on the behavior of zeros of Hermite–Padé approximations for a set of exponential functions $\{e^{pz}\}_{p=0}^k$.