### A Curvilinear Cluster Set Uniqueness Theorem for Meromorphic Functions.

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We give an upper estimate of Petrenko's deviation for a meromorphic function of finite lower order in terms of Valiron's defect and the number p(∞,f) of separated maximum modulus points of the function. We also present examples showing that this estimate is sharp.

A dual transformation is discussed, by which a concurrent chart represented by one equation is transformed into an alignment chart or into a tangential contact chart. Using this transformation an alignment chart where three scales coincide and a tangential contact chart consisting of a family of circles, which represent the relation $u+v+w=0$, are constructed. In this case, a form of the addition-theorem for Weierstrass’ function involving no derivative is used.

We deal with the uniqueness of analytic functions in the unit disc sharing four distinct values and obtain two theorems improving a previous result given by Mao and Liu (2009).

In this paper we study the comparative growth properties of a composition of entire and meromorphic functions on the basis of the relative order (relative lower order) of Wronskians generated by entire and meromorphic functions.