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
$$F(x, y)=bs 0 {m_1} A_k(y)x^{m_1-k}mbox{ and } G(x, y)=bs 0 {m_2} B_k(y)x^{m_2-k}$$
with entire functions $A_k(y), B_k(y)$.
We    derive a priory estimates  for the sums of the roots
of the considered system and
for the counting function of  roots.

Keywords