Difference Picard theorem for meromorphic functions of several variables

Details Difference Picard theorem for meromorphic functions of several variables Difference Picard theorem for meromorphic functions of several variables

2009-03-23

arxiv.org/abs/0903.3857v1

Mathematics

Complex Variables

19 pages

Scientific paper

It is shown that if three distinct values of a meromorphic function f:C^n -> P^1 of hyper-order strictly less than 2/3 have forward invariant pre-images with respect to a translation t:C^n -> C^n, t(z)=z+c, then f is a periodic function with period c. This result can be seen as a generalization of M. Green's Picard-type theorem in the special case where the hyper-order of f is less than 2/3, since the empty pre-images of the usual Picard exceptional values are by definition always forward invariant. In addition, difference analogues of the lemma on the logarithmic derivative and of the second main theorem of Nevanlinna theory for meromorphic functions C^n -> P^1 are given, and their applications to partial difference equations are discussed.

Affiliated with

Also associated with

No associations

Rating

Difference Picard theorem for meromorphic functions of several variables does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Difference Picard theorem for meromorphic functions of several variables, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Difference Picard theorem for meromorphic functions of several variables will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-346562