### Coupled systems of equations with entire and polynomial functions

Author

Department of Mathematics, Ben Gurion University of the Negev

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