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 rootsof the considered system andfor the counting function of  roots.

in this paper, we show that for any finite order entire function $f(z)$, the function of the form $f(z)^{n}[f(z+c)-f(z)]^{s}$ has no nonzero finite picard exceptional value for all nonnegative integers $n, s$ satisfying $ngeq 3$, which can be viewed as a different result on hayman conjecture. we also obtain some uniqueness theorems for difference polynomials of entire functions sharing one comm...

If f is an entire function and a complex number, said to be asymptotic value of if there exists path $$\gamma $$ from 0 infinity such that $$f(z) - a$$ tends as z along . The Denjoy–Carleman–Ahlfors Theorem asserts has n distinct values, then the rate growth at least order n/2, mean type. A long-standing problem asks whether this conclusion holds for functions having (entire) functions, each mo...