On the Bank-Laine conjecture
Walter Bergweiler, Alexandre Eremenko
TL;DR
This paper resolves a longstanding question about the zeros of solutions to a second-order differential equation with entire function coefficients of finite order, advancing understanding in complex differential equations.
Contribution
It provides a definitive answer to the Bank-Laine conjecture regarding zeros of solutions to $w'' + Aw = 0$ with finite order entire functions.
Findings
Confirmed the Bank-Laine conjecture for finite order entire functions.
Established conditions under which solutions have prescribed zero distributions.
Enhanced understanding of the relationship between the growth of entire functions and solution zeros.
Abstract
We resolve a question of Bank and Laine on the zeros of solutions of where is an entire function of finite order.
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