Exponential polynomials in the oscillation theory

Abstract Supposing that A ( z ) is an exponential polynomial of the form A ( z ) = H 0 ( z ) + H 1 ( z ) e ζ 1 z n + ⋯ + H m ( z ) e ζ m z n , where H j 's are entire and of order H 0 ( z ) and the geometric location of the leading coefficients ζ 1 , … , ζ m 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 Phragmen-Lindelof indicator function. In addition to results in the whole complex plane, results on sectorial oscillation are proved.