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Quantitative subspace theorem and general form of second main theorem for higher degree polynomials

Abstract

This paper deals with the quantitative Schmidt’s subspace theorem and the general from of the second main theorem, which are two correspondence objects in Diophantine approximation theory and Nevanlinna theory. In this paper, we give a new below bound for Chow weight of projective varieties defined over a number field. Then, we apply it to prove a quantitative version of Schmidt’s subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety. Finally, we apply this new below bound for Chow weight to establish a general form of second main theorem in Nevanlinna theory for meromorphic mappings into projective varieties intersecting hypersurfaces in subgeneral position with a short proof. Our results improve and generalize the previous results in these directions.

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Acknowledgements

We would like to thank the referee for carefully reading our manuscript and for his/her valuable comments on the first version of this paper, which help us to improve the quality of the paper.

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Correspondence to Duc Quang Si.

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Dedicated to Professor Le Mau Hai on the occasion of His 70th birthday.

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Si, D.Q. Quantitative subspace theorem and general form of second main theorem for higher degree polynomials. manuscripta math. (2021). https://doi.org/10.1007/s00229-021-01329-z

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Mathematics Subject Classification

  • Primary 11J68
  • 32H30
  • Secondary 11J25
  • 11J97
  • 32A22