Tropical Nevanlinna theory and second main theorem

We present a version of the tropical Nevanlinna theory for real-valued, continuous, piecewise linear functions on the real line. In particular, a tropical version of the second main theorem is proved. Applications to some ultra-discrete equations are given.Comment: 43 pages, 3 figure

New findings on the periodicity of entire functions and their differential polynomials

In this paper, we seek to explore under what conditions the periodicity of an entire function $f(z)$ follows from the periodicity of a differential polynomial in $f(z)$. We improve and generalize some earlier results and we give other new findings.Comment: 15 page

Riccati differential equations with elliptic coefficients II

We study a Riccati differential equation whose coefficient is expressible in terms of a special Weierstrass pe-function. We show that all the solutions are meromorphic, and examine the periodicity of them.We study a Riccati differential equation whose coefficient is expressible in terms of a special Weierstrass pe-function. We show that all the solutions are meromorphic, and examine the periodicity of them