arXiv subjects

Sanjay Mallick

Publications and source records attributed to Sanjay Mallick.

3 recordsLinked to original sources

arXiv2025

A General Characterization on the Uniqueness Problem of L-Functions and General Meromorphic Functions

In the paper, concerning a question of Yi [23], we study general criterion for the uniqueness of an L-function and a general meromorphic function. Our results improve and extend all the existing results in this direction [23, 18, 17, 4] to the most general setting. Moreover, we have exhibited a handsome number of examples to justify our claims as well as to confirm the wide-ranging applications of our results.

math.CV↗

arXiv2025

On the characterization of uniqueness polynomials: both complex and p-adic versions

The problem "A general characterization of uniqueness polynomial for non-critically injective polynomials" has been remained open since the last two decades. In this paper, we explore this open problem. To this end, we initiate a new approach that also includes critically injective polynomials. We provide this characterization for both the complex and p-adic cases. We also provide various examples as an application of our results along with the verification of the existing examples. Consequently, we find examples of unique range sets generated by non-critically injective polynomials with least cardinalities achieved so far and one of these results is sharp with respect to all the available formulas in the literature. Furthermore, we cover the part of least degree uniqueness polynomials. In this part, we also provide some sharp bounds.

math.CV↗

arXiv2024

Gateaux differentiability in the Banach space of meromorphic functions

We study the Gateaux differentiability in the Banach space of meromorphic functions and obtain a complete characterization of the same, by using Birkhoff-James orthogonality techniques. We introduce the concept of extended orthogonality covering set (EOCS), which allows us to present refinements of some earlier results on the Gateaux differentiability of analytic functions. We also discuss some related properties of meromorphic functions which follow directly from the said characterization.

math.CV↗