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A finite-order answer to a problem of Erdős on maximum modulus points
Leticia Pardo-Simón, David J. Sixsmith
In 1964, Erdős asked whether, for a non-monomial entire function, the number of maximum modulus points on the circle \(|z|=r\) can become arbitrarily large as . In 1968…
On a result of Hayman concerning the maximum modulus set
Vasiliki Evdoridou, Leticia Pardo-Simón, David J. Sixsmith
The set of points where an entire function achieves its maximum modulus is known as the maximum modulus set. In 1951, Hayman studied the structure of this set near the origin. Foll…
The maximum modulus set of a polynomial
L. Pardo-Simón, D. J. Sixsmith
We study the maximum modulus set, , of a polynomial . We are interested in constructing so that has certain exceptional features. Jassim and…
Variations on a theme of Hardy concerning the maximum modulus
L. Pardo-Simón, D. J. Sixsmith
In 1909, Hardy gave an example of a transcendental entire function, , with the property that the set of points where achieves its maximum modulus, , has infi…