Tropical second main theorem and the Nevanlinna inverse problem

Galina Filipuk; Juho Halonen; Risto Korhonen

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Tropical second main theorem and the Nevanlinna inverse problem

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arxiv 2305.13939 v1 pith:PXZOQDSD submitted 2023-05-05 math.AG math.CV

Juho Halonen , Risto Korhonen , Galina Filipuk This is my paper · ORCID

classification math.AGmath.CV

keywords tropicalnevanlinnafunctionshypersurfacesinversemainproblemsecond

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A generalization of the second main theorem of tropical Nevanlinna theory is presented for noncontinuous piecewise linear functions and for tropical hypersurfaces without requiring a growth condition. The method of proof is novel and significantly more straightforward than previously known proofs. The tropical analogue of the Nevanlinna inverse problem is formulated and solved for tropical meromorphic functions and tropical hypersurfaces.

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