In 1879, Picard established the well-known and beautiful result that a transcen-
dental entire function assumes all values infinitely often with one exception. Since
then Hadamard (1893), Borel (1897) and Blumenthal (1910) had tried to give Pi-
card’s result a quantitative description and extend it to meromorphic functions.
It was R. Nevanlinna, who achieved such an attempt in (1925) by establishing the
so-called value distribution theory of meromorphic functions which was praised
by H. Weyl (1943) as “One of the few great mathematical events of our century”.
Moreover, part of the significance of Nevanlinna’s approach is that the concept
of exceptional values can be given a geometric interpretation in terms of geomet-
ric objects like curves and mappings of subspaces of holomorphic curves from a
n
complex plane C to a projective space P . In the years since these results were achieved, mathematicians of comparable stature have made efforts to derive an analogous theory for meromorphic mappings and p-adic meromorphic functions. Besides the value distribution, the theory has had many applications to the an- alyticity, growth, existence, and unicity properties of meromorphic solutions to differential or functional equations. More recently, it has been found that there is a profound relation between Nevanlinna theory and number theory.