Asymptotic distributions of zeros of quadratic Hermite-Pade polynomials associated with the exponential function

The asymptotic distributions of zeros of the quadratic Hermite-Pade polynomials pn, q(n), r(n) is an element of P-n associated with the exponential function are studied for n -> infinity o. The polynomials are defined by the relation (*) p(n) (z) + q(n) (z)e(z) + r(n) (z)e(2z) = O (z(3n+2)) as z -> 0, and they form the basis for quadratic Hermite-Pade approxiniants to e(z). In order to achieve a differentiated picture of the asymptotic behavior of the zeros, the independent variable z is rescaled in such a way that all zeros of the polynomials p(n), q(n), r(n) have finite cluster points as n -> infinity. The asymptotic relations, which are proved, have a precision that is high enough to distinguish the positions of individual zeros. In addition to the zeros of the polynomials p(n), q(n), r(n), also the zeros of the remainder term of (*) are studied. The investigations complement asymptotic results obtained in [17].