Binary forms, equiangular polygons and harmonic measure

DOI10.1216/rmjm/1022008975zbMath0977.11017OpenAlexW2041279243MaRDI QIDQ5928658

Richard Snyder Laugesen, Michael A. Bean

Publication date: 1 April 2001

Published in: Rocky Mountain Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://math.la.asu.edu/~rmmc/rmj/VOL30-1/CONT30-1/CONT30-1.html

zbMATH Keywords

Beta functionDiophantine inequalityharmonic radiusisoperimetric inequalitiesLagrangian planeSchwarz-Christoffel transformations

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Conformal mappings of special domains (30C20) Diophantine inequalities (11D75) Diophantine inequalities (11J25) Extremal problems for conformal and quasiconformal mappings, variational methods (30C70) Capacity and harmonic measure in the complex plane (30C85) Length, area and volume in real or complex geometry (51M25)

Related Items (3)

On the representation of integers by binary forms defined by means of the relation \((x + yi)^n= R_n(x,y) + J_n(x,y)i\) ⋮ ON THE AREA OF THE FUNDAMENTAL REGION OF A BINARY FORM ASSOCIATED WITH ALGEBRAIC TRIGONOMETRIC QUANTITIES ⋮ On the area bounded by the curve \(\prod_{k = 1}^n|x\sin\frac{k\pi}{n} - y\cos\frac{k\pi}{n}|=1\)

Cites Work

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• Integral inequalities for algebraic polynomials with a restriction on their zeros
• Density of integer points on affine homogeneous varieties
• An extremal property of meromorphic functions withn–fold symmetry
• An isoperimetric inequality related to Thue’s equation
• The practical computation of areas associated with binary quartic forms
• A Note on the Thue Inequality
• Binary Forms, Hypergeometric Functions and the Schwarz-Christoffel Mapping Formula
• Harmonic Radius and Concentration of Energy; Hyperbolic Radius and Liouville’s Equations $\Delta U = e^U $ and $\Delta U = U^{\tfrac{{n + 2}}{{n - 2}}} $

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