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.
citing papers explorer
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On the rational solutions of generalized Abel equations
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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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.
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Some factorization results for formal power series
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.