Abstract

Supposing that A(z) is an exponential polynomial of the formA(z)=H0(z)+H1(z)eζ1zn+⋯+Hm(z)eζmzn, where Hj's are entire and of order <n, it is demonstrated that the function H0(z) and the geometric location of the leading coefficients ζ1,…,ζm play a key role in the oscillation of solutions of the differential equation f″+A(z)f=0. The key tools consist of value distribution properties of exponential polynomials, and elementary properties of the Phragmén-Lindelöf indicator function. In addition to results in the whole complex plane, results on sectorial oscillation are proved.

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