Every nonconstant rational solution is of the form x=1/p(t), with S bounded by (n2-1)+2(n3-1) over C and by 12 over R under nondegeneracy.
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New elementary proofs establish complete Kobayashi hyperbolicity for the twice-punctured plane and bounded planar domains without using the disk cover or negative curvature, with applications to Picard-type theorems and a Hahn-inspired characterization.
Factorization theorems with sharp bounds and an extension of the Dumas irreducibility criterion to formal power series over PIDs and DVRs using Newton polygons and constant term factorizations.
A proof of the uniformization theorem for domains in the Riemann sphere is given via the Kobayashi metric without relying on the elliptic modular function.
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Revisiting Kobayashi hyperbolicity on planar domains
New elementary proofs establish complete Kobayashi hyperbolicity for the twice-punctured plane and bounded planar domains without using the disk cover or negative curvature, with applications to Picard-type theorems and a Hahn-inspired characterization.