• Corpus ID: 119174169

# Mason's theorem with a difference radical

```@article{Ishizaki2018MasonsTW,
title={Mason's theorem with a difference radical},
author={Katsuya Ishizaki and Risto Korhonen and Nan Li and Kazuya Tohge},
journal={arXiv: Complex Variables},
year={2018}
}```
Differential calculus is not a unique way to observe polynomial equations such as \$a+b=c\$. We propose a way of applying difference calculus to estimate multiplicities of the roots of the polynomials \$a\$, \$b\$ and \$c\$ satisfying the equation above. Then a difference \$abc\$ theorem for polynomials is proved using a new notion of a radical of a polynomial. Two results on the non-existence of polynomial solutions to difference Fermat type functional equations are given as applications. We also…

## References

SHOWING 1-10 OF 16 REFERENCES
Zeros of analytic functions, with or without multiplicities
The classical Mason–Stothers theorem deals with nontrivial polynomial solutions to the equation a + b = c. It provides a lower bound on the number of distinct zeros of the polynomial abc in terms of
Holomorphic curves with shift-invariant hyperplane preimages
• Mathematics
• 2009
If f : C ! P n is a holomorphic curve of hyper-order less than one for which 2n + 1 hyperplanes in general position have forward invariant preimages with respect to the translation �(z) = z +c, then
Old and new conjectured diophantine inequalities
The original meaning of diophantine problems is to find all solutions of equations in integers or rational numbers, and to give a bound for these solutions. One may expand the domain of coefficients
An Alternate Proof of Mason's Theorem
Noah Snyder is an undergraduate student at Harvard University. He plans on continuing in mathematics in both graduate school and as a career. At present he is most interested in Number Theory. He
The Strength of Cartan's Version of Nevanlinna Theory
• Mathematics
• 2004
In 1933 Henri Cartan proved a fundamental theorem in Nevanlinna theory, namely a generalization of Nevanlinna’s second fundamental theorem. Cartan’s theorem works very well for certain kinds of
Waring’s theorem and the super Fermat problem for numbers and functions
Assume that , are positive intergers. Waring’s problem, first proved by Hilbert, asserts that every sufficiently large can be expressed as the sum of at most nth powers. The Super-Fermat problem asks
Diophantine Equations Over Function Fields
Preface 1. The fundamental inequality 2. The Thue equation 3. The hyperelliptic equation 4. Equations of small genus 5. Bounds for equations of small genus 6. Fields of arbitrary characteristics 7.
A note on the abc conjecture
• Mathematics
• 2002
In this note we have generalized the abc-conjecture for integers and extended Mason's theorem to polynomials in ℂm by dint of Nevanlinna's value distribution theory. © 2002 Wiley Periodicals, Inc.
Note on the ABC Conjecture
This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into
Fermat’s last theorem for polynomials, Parabola
• 1999