Given a projective variety X defined over a finite field, the zeta function of divisors counts all irreducible, codimension one subvarieties of X, each measured by their projective degree. For dim(X) ≥ 2, this is a purely p-adic function. Four conjectures are expected to hold, the first of which is p-adic meromorphic continuation to the all of Cp. When the divisor class group of X has rank one,...

A new denition of the incomplete beta function as a distribution- valued meromorphic is given and finite parts it its partial derivatives at singular values are calculated compared with formulas in literature.

Meromorphic solutions of non-linear differential equations the form f n + P ( z , ) = h are investigated, where ? 2 is an integer, a meromorphic function, and polynomial in its derivatives with small functions as coefficients. In existing literature this equation has been studied case when particular p 1 e ? entire functions. such order either positive integer or equal to infinity. article it a...

This research concentrates on the analysis of meromorphic mappings. We derived several important results for value distribution of specific difference polynomials of meromorphic mappings, which generalize the work of Laine and Yang. In addition, we proved uniqueness theorems of meromorphic mappings. The difference polynomials of these functions have the same fixed points or share a nonzero valu...

In this paper, we have found the most generalized form of famous Frank-Reinders polynomial. With help same, investigated on unique range set meromorphic function under two smallest possible weights namely 0 and 1. Our results extend some existing in literature.

Recommended by Narendra Kumar Govil This article deals with problems of the uniqueness of transcendental meromorphic function with shared values in some angular domains dealing with the multiple values which improve a result of J. Zheng.

In this paper, we investigate the problem of the uniqueness of meromorphic function sharing values. It is turned out that our results are natural extensions of Q. C. Zhang and G. G. Gundersen.

A boundary version of the Schwarz lemma for meromorphic functions is investigated. For function Inf(z) = 1/z +?? k=2 knck?2zk?2, belonging to class W, we estimate from below modulus angular derivative on point unit disc.

The Fourier coefficients of the non-holomorphic Eisenstein cusp forms Laplace-Beltrami operator are here summed. summation is performed after Dirichlet series related to divisor function, properties meromorphic continuability; a new dependence on Euler’s γ constant also found.

We construct a new exact solution of Einstein's equations in vacuo in terms of Weyl canonical coordinates. This solution may be interpreted as a black hole in a space-time which is periodic in one direction and which behaves asymptotically like the Kasner solution with Kasner index equal to 4M L −1 , where L is the period and M is the mass of the black hole. Outside the horizon, the solution is...