The classical representation problem for a meromorphic function <$E f> in <$E {roman C back 55 roman I} sup n>, consists in representing <$E f> as the quotient <$E f~=~g "/" h> of two entire functions <$E g> and <$E h>, each with logarithm of modulus majorized by a function as close as possible to the Nevanlinna characteristic. Here we introduce generalizations of the Nevanlinna characteristic and give a short survey of classical and recent results on the representation of a meromorphic function in terms such characteristics. When <$E f> has a finite lower order, the Paley problem on best possible estimates of the growth of entire functions <$E g> and <$E h> in the representations <$E f~=~g "/" h> will be considered. Also we point out to some unsolved problems in this area.

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