Coupled systems of equations with entire and polynomial functions

Gil, M.

doi:10.22075/ijnaa.2012.50

Coupled systems of equations with entire and polynomial functions

Document Type : Research Paper

Author

M. Gil

Department of Mathematics, Ben Gurion University of the Negev

10.22075/ijnaa.2012.50

Abstract

We consider the coupled system $F(x,y)=G(x,y)=0$, where
$$
F(x, y)=\sum_{k=0}^{m_1} A_k(y)x^{m_1-k} \quad \text{ and }\quad G(x, y)=\sum_{k=0}^{m_2} B_k(y)x^{m_2-k}
$$
with entire functions $A_k(y), B_k(y)$. We derive a priory estimate for the sums of the roots of the considered system and for the counting function of roots.

Keywords

coupled systems

entire and polynomial functions

a priory estimates

resultant