高次多项式情形下子空间定理的一个推广

A generalization of the subspace theorem for higher degree polynomials in subgeneral position

In this paper, we prove a generalization of the Schmidt's subspace theorem for polynomials of higher degree in subgeneral position with respect to a projective variety over a number field. Our result improves and generalizes the previous results on Schmidt's subspace theorem for the case of higher degree polynomials.

Polynomial Values in Affine Subspaces of Finite Fields

In this paper we introduce a new approach and obtain new results for the problem of studying polynomial images of affine subspaces of finite fields. We improve and generalise several previous known results, and also extend the range of such results to polynomials of degrees higher than the characteristic of the field. Such results have a wide scope of applications similar to those associated with their counterparts studying consecutive intervals over prime fields instead of affine subspaces. Here we give only two immediate consequences: to a bound on the size of the intersection of orbits of p…

A generalization of effective schmidt's subspace theorem for projective varieties over function fields

We establish an effective version of Schmidt's subspace theorem on a smooth projective variety $\mathcal{X}$ over function fields of characteristic zero for hypersurfaces located in m-subgeneral position with respect to $\mathcal{X}$. Our result generalizes and improves the results of An-Wang, Ru-Wang and the author.

Schmidt子空间定理的一些推广

Some generalizations of Schmidt's subspace theorem

本文给出了Schmidt子空间定理针对任意高次多项式族的定量版本，并针对射影代数簇中任意闭子概形族提出了该定理的推广。

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

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…

Polynomial Values in Subfields and Affine Subspaces of Finite Fields

For an integer $r$, a prime power $q$, and a polynomial $f$ over a finite field ${\mathbb F}_{q^r}$ of $q^r$ elements, we obtain an upper bound on the frequency of elements in an orbit generated by iterations of $f$ which fall in a proper subfield of ${\mathbb F}_{q^r}$. We also obtain similar results for elements in affine subspaces of ${\mathbb F}_{q^r}$, considered as a linear space over ${\mathbb F}_q$.