A remark on Zagier's observation of the Mandelbrot set

zbMath1352.37142arXiv1306.6140MaRDI QIDQ888450

Hirokazu Shimauchi

Publication date: 30 October 2015

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1306.6140

zbMATH Keywords

Mandelbrot set\(p\)-adic valuation of Laurent coefficientsunicritical polynomial

Mathematics Subject Classification ID

Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10)

Related Items (3)

Coefficients of the Riemann map for the Mandelbrot set complement ⋮ Taylor Coefficients of the Conformal Map for the Exterior of the Reciprocal of the Multibrot Set ⋮ The area of the Mandelbrot set and Zagier's conjecture

Cites Work

• The uniformization of the complement of the Mandelbrot set
• The area of the Mandelbrot set
• A proof of Thurston's topological characterization of rational functions
• Computing the Laurent series of map \(\Psi:C-\overline D\to C-M\)
• Symmetries of fractals revisited
• On the coefficients of the mapping to the exterior of the Mandelbrot set
• On the arithmetic properties of a certain sequence of polynomials
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