Nevanlinna Theory, Diophantine Approximation, and Numerical Analysis.
Nevanlinna theory for the difference operator.
Nevanlinna theory, Fuchsian functions and Brownian motion windings.
Atsuji proposed some integrals along Brownian paths to study the Nevanlinna characteristic function T(f,r) when f is meromorphic in the unit disk D. We show that his criterios does not apply to the basic case when f is a modular elliptic function. The divergence of similar integrals computed along the geodesic flow is also proved. (A)
New polynomials for which has a solution with almost all real zeros.
Nonlinear differential monomials sharing two values
Using the notion of weighted sharing of values which was introduced by Lahiri (2001), we deal with the uniqueness problem for meromorphic functions when two certain types of nonlinear differential monomials namely
Nonlinear differential polynomials sharing a non-zero polynomial with finite weight
In the paper, dealing with a question of Lahiri (1999), we study the uniqueness of meromorphic functions in the case when two certain types of nonlinear differential polynomials, which are the derivatives of some typical linear expression, namely (), share a non-zero polynomial with finite weight. The results obtained in the paper improve, extend, supplement and generalize some recent results due to Sahoo (2013), Li and Gao (2010). In particular, we have shown that under a suitable choice of...
Nonlinear differential polynomials sharing a small function
Nonlinear differential polynomials sharing a small function
Dealing with a question of Lahiri [6] we study the uniqueness problem of meromorphic functions concerning two nonlinear differential polynomials sharing a small function. Our results will not only improve and supplement the results of Lin-Yi [16], Lahiri Sarkar [12] but also improve and supplement a very recent result of the first author [1].
Normal families and shared values of meromorphic functions.
Normality and value sharing with a linear differential polynomial
We prove some normality criteria for a family of meromorphic functions and as an application we prove a value distribution theorem for a differential polynomial.
Normality criteria for families of zero-free meromorphic functions
Let ℱ be a family of zero-free meromorphic functions in a domain D, let n, k and m be positive integers with n ≥ m+1, and let a ≠ 0 and b be finite complex numbers. If for each f ∈ ℱ, has at most nk zeros in D, ignoring multiplicities, then ℱ is normal in D. The examples show that the result is sharp.
Normality criterion concerning sharing functions. II.
Normality of composite analytic functions and sharing an analytic function.
Note on the normal family.
Notes on a generalized -conjecture over function fields