Tam'as Erd'elyi

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math.NT2025

The sequence of partial sums of a unimodular power series is not ultraflat

TamÃ¡s ErdÃ©lyi

We show that if $(a_{j})_{j = 0}^{\infty}$ is a sequence of numbers $a_{j} \in C$ with $∣ a_{j} ∣ = 1$ , and $P_{n} (z) = j = 0 \sum n a_{j} z^{j}, n = 0, 1, 2, \dots,$ then $(P_{n})$ is N…

math.NT2024

Extensions of the Bloch-PÃ³lya theorem on the number of real zeros of polynomials (II)

We prove that there is an absolute constant $c > 0$ such that for every $a_{0}, a_{1}, \dots, a_{n} \in [1, M], 1 \leq M \leq \frac{1}{4} exp (\frac{n}{9}),$ there are…