Univalent functions with half-integral coefficients

Naoki Hiranuma; Toshiyuki Sugawa

doi:10.1007/s40315-013-0009-z

Univalent functions with half-integral coefficients

Naoki Hiranuma, Toshiyuki Sugawa

INF - Computer and Mathematical Sciences

Sumitomo Life Insurance

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

Abstract

B. Friedman discovered in his 1946 paper that the set of analytic univalent functions on the unit disk in the complex plane with integralTaylor coefficients consists of nine functions. In the present paper, we prove that the similar set obtained by replacing "integral" by "half-integral" consists of another 12 functions in addition to the nine. We also observe geometric properties of the 12 functions.

Original language	English
Pages (from-to)	133-151
Number of pages	19
Journal	Computational Methods and Function Theory
Volume	13
Issue number	1
DOIs	https://doi.org/10.1007/s40315-013-0009-z
Publication status	Published - 2013 May

Keywords

Area theorem
Grunsky inequality

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10.1007/s40315-013-0009-z

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keywords = "Area theorem, Grunsky inequality",

author = "Naoki Hiranuma and Toshiyuki Sugawa",

note = "Funding Information: The present research was supported in part by JSPS Grant-in-Aid for Scientific Research (B) 22340025 and contains part of Master{\textquoteright}s thesis of the first author.",

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AU - Sugawa, Toshiyuki

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N2 - B. Friedman discovered in his 1946 paper that the set of analytic univalent functions on the unit disk in the complex plane with integralTaylor coefficients consists of nine functions. In the present paper, we prove that the similar set obtained by replacing "integral" by "half-integral" consists of another 12 functions in addition to the nine. We also observe geometric properties of the 12 functions.

AB - B. Friedman discovered in his 1946 paper that the set of analytic univalent functions on the unit disk in the complex plane with integralTaylor coefficients consists of nine functions. In the present paper, we prove that the similar set obtained by replacing "integral" by "half-integral" consists of another 12 functions in addition to the nine. We also observe geometric properties of the 12 functions.

KW - Area theorem

KW - Grunsky inequality

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SP - 133

EP - 151

JO - Computational Methods and Function Theory

JF - Computational Methods and Function Theory

IS - 1

ER -

Univalent functions with half-integral coefficients

Abstract

Keywords

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