�ber die Nullstellen von L�sungen linearer Differentialgleichungen

On the oscillation of solutions of certain linear differential equations in the complex domain

“…It now follows from (4.9), (4.10), (4.11) and the representation f=Tl 1 (4.25) and where the total degrees of Bj and B 2 are at most k-2. We need estimates for the derivatives of G' on the ray arg z = 9 2 which we obtain as follows.…”

“…The same conclusions hold if y" is replaced by a higher derivative in (1.1). Denoting by a(g) the order of an entire function g, and by k(g) the exponent of convergence of its zeros we have the following, proved in [1,3]:…”

A remark on distribution of zeros of solutions of linear differential equations

“…Let wx and w2 be two independent solutions of SDE (1). If A(z) is not a constant, then the zeros of E = wxwi are attracted to a system of rays Dq = D(0it, 0j2, ... , 0im) (0 < i\ < i% < • • • < im < n + 1) having the same form as in (2) with the properties that for each 6\ and arbitrary small e > 0, Vik(e) contains infinitely many zeros of E, ■co(D0) = ^±1 = p(wx) -p(w2), and m>2.…”

“…[7,2,16]) that the result of Frank remains true if PEV 0 is replaced by BEV 0. This has been proved independently by Brüggemann [4] and Steinmetz [14]; the other is the Hellerstein-Rossi conjecture (cf.…”

“…Let w(z) be a transcendental solution of SDE (1). Write A(z) -a"z" + -\-oq , an^0, and set (2) 9j=2n(j+^arga^ J = 0¡u2>__n+L Lemma 2 in [10] asserts that if w(z) has infinitely many zeros in Vj(e) for some j, then the number of those zeros is n (r, Vj(e), 1) = (1 + 0{\))^r", P = ^ = P(w).…”