We prove some uniqueness theorems for meromorphic functions sharing three values with some weight which improve some known results.

* Correspondence: [email protected]; [email protected] School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China School of Economic and Management, Guangzhou University of Chinese Medicine, Guangzhou 510006, China Full list of author information is available at the end of the article Abstract In the article, we study the normality of families of meromorphic ...

On the face of it, part (i) is a particular case of part (ii), and the latter part of (iii), but actually all three parts are algebraically equivalent by the following elementary argument. For given periods, we introduce the closed Riemann surface V2 of genus p = l on which our meromorphic functions are suitably defined, and we take it as known that on such or any other closed Riemann surface o...

Let f be a meromorphic, transcendental function in the finite plane having a finite number of a-points. The well-known theorem of Iversen [i, p. 224] asserts that in this case there exists a curve F going out to such that f(z) -~ a as z ~ ~, z ~ F. Such a curve is called an asymptotic curve. We henceforth make use of the standard notation from the theory of meromorphic functions [1] without spe...

We calculate the local Fourier transformations for a class of Ql-sheaves. In particular, we verify a conjecture of Laumon and Malgrange ([15] 2.6.3). As an application, we calculate the local monodromy of l-adic hypergeometric sheaves introduced by Katz ([12]). We also discuss the characteristic p analogue of the Turrittin-Levelt Theorem for D-modules. The method used in this paper can be used ...

is a weight k ∈ 2Z meromorphic modular form on SL2(Z). It is well known that f(z) is distinguished by its weight k and its “first few coefficients”. The Riemann-Roch Theorem provides the number of coefficients which are sufficient for distinguishing such a form f(z). Here we obtain a combinatorial extension of this classical fact; specifically, we give universal recursion relations which produc...

If f(z) is a weight k ∈ 1 2 Z meromorphic modular form on Γ0(N) satisfying f(z) = ∑

We classify the completely integrable systems associated with classical root systems whose potential functions are meromorphic at an infinite point.

Considering the uniqueness of meromorphic functions concerning differential monomials ,we obtain that, if two non-constant meromorphic functions   f z and   g z satisfy     1, 1, n n k k E f f E g g    , where k and n are tow positive integers satisfying 3 k  and 11 n  , then either     1 2 , cz cz z z f c e g c e    where 1 c , 2 c , c are three constants, satisfying   1 ...