Coupled systems of equations with entire and polynomial functions


Department of Mathematics, Ben Gurion University of the Negev


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.