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- W4287553288 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." @default.
- W4287553288 created "2022-07-25" @default.
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- W4287553288 date "2020-12-14" @default.
- W4287553288 modified "2023-10-18" @default.
- W4287553288 title "On a result of Hayman concerning the maximum modulus set" @default.
- W4287553288 doi "https://doi.org/10.48550/arxiv.2012.07409" @default.
- W4287553288 hasPublicationYear "2020" @default.
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