Abstract:The study of the asymptotic behavior of an entire transcendental function of the form f(z) = Pn anzpn, pn ∈ N, on curves γ going to infinity arbitrarily, is a classical problem, goes back to the works of Hadamard, Littlewood and Polia. Polia posed the following problem: under what conditions on pn does there unbounded sequence {ξn} ⊂ γ exist such that lnMf(|ξn|) ∼ ln|f(ξn)| for ξn → ∞ (Polya’s problem). Here Mf(r) is the maximum of the modulus f on a circle of radius r. He showed that if the sequence {pn} has … Show more
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