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Generalized slow growth of special monogenic functions

Kumar S.

Journal of Applied Analysis

2016

Vol. 22, nr 1

67--79

In the present paper we study the generalized slow growth of special monogenic functions. The characterizations of generalized order, generalized lower order, generalized type and generalized lower type of special monogenic functions have been obtained in terms of their Taylor series coefficients.

On the generalized order and generalized type of entire monogenic functions

Srivastava G. S., Kumar S.

Demonstratio Mathematica

2013

Vol. 46, nr 4

663--677

In the present paper we study the generalized growth of entire monogenic functions. The generalized order, generalized lower order and generalized type of entire monogenic functions have been obtained in terms of its Taylor’s series coefficients.

Polynomial imaginary decompositions for finite extensions of fields of characteristic zero

Nowicki A., Spodzieja S.

Bulletin of the Polish Academy of Sciences. Mathematics

2003

Vol. 51, no 2

157-168

Let k be a field of characteristic zero, L = k[xi] a finite field extension of k of degree m > 1. If f is a polynomial in one variable over L, then there exist unique polynomials u0,..., um-1 belonging to k[x0,..., xm-l] such that f(x0 + xix1 + ...xi^m-1 xm-l) = uO + xiu1 + ...xi^m-1 um-1. We prove that for u0, ..., um-1is an element of k[xo,..., xm-1) there exists f for which the above holds if and only if u0, ..., um-1satisfy some generalization of the Cauchy-Riemann equations. Moreover, we show that if f is not an element of L, then the polynomials u0, ... ,um-1 are algebraically independent over k and they have no common divisors in k[xo,... ,Xm-1) of positive degree. Some other properties of polynomials u0,..., um-1 are also given.