A generalized äbc" conjecture over function fields
by
Chung-Chun Yang
Hong Kong University of Science and Technology
Coauthors: Pei-Chu Hu (Shandong University, Jinan China)

Mason's theorem says ``Let a(z), b(z) and c(z) be relatively prime polynomials in a field \kappa not all constants such that a+b=c. Then

max {deg(a), deg(b), deg(c)} <= n   (\frac1abc)-1,

where [`n](\frac1x) denotes the number of distinct zeros of x. ``abc" conjecture says that given \epsilon > 0, there exists a number C(\epsilon) having the following property: for any non-zero relative prime numbers a, b and c such that a+b=c,

max {|a|, |b|, |c|} <= C(\epsilon) N   (\frac1abc)1+\epsilon,

where [`N](\frac1x) denotes the product of distinct prime factors of an integer x.

In this paper, we suggest a generalized version of ``abc" conjecture, and prove its analogues for non-Archimedean entire functions, as well as a generalized Mason's theorem on polynomials.

Date received: May 15, 1999

Copyright © 1999 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cacl-11.