Tam'as Erd'elyi

collaborators

3 papers

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)

TamÃ¡s ErdÃ©lyi

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…

math.CA2024

The number of real zeros of polynomials with constrained coefficients

We prove that there is an absolute constant $c > 0$ such that every polynomial $P$ of the form $$P(z) = \sum_{j=0}^{n}{a_jz^j}\,, \quad |a_0| = 1\,, \quad |a_j| \leq M\,, \quad a_j…