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Evdoridou, Vasiliki; Pardo-Simón, Leticia and Sixsmith, David J.
(2021).
DOI: https://doi.org/10.1007/s40315-021-00407-3
Abstract
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. Following work of Blumenthal, he showed that, near zero, the maximum modulus set consists of a collection of disjoint analytic curves, and provided an upper bound for the number of these curves. In this paper, we establish the exact number of these curves for all entire functions, except for a “small” set whose Taylor series coefficients satisfy a certain simple, algebraic condition. Moreover, we give new results concerning the structure of this set near the origin, and make an interesting conjecture regarding the most general case. We prove this conjecture for polynomials of degree less than four.
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- Item ORO ID
- 78421
- Item Type
- Journal Item
- ISSN
- 1617-9447
- Academic Unit or School
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Faculty of Science, Technology, Engineering and Mathematics (STEM) > Mathematics and Statistics
Faculty of Science, Technology, Engineering and Mathematics (STEM) - Copyright Holders
- © 2021 Vasiliki Evdoridou, © 2021 Leticia Pardo-Simón, © 2021 David J. Sixsmith
- Depositing User
- ORO Import