M.Sc Thesis | |

M.Sc Student | Segol Nimrod |
---|---|

Subject | Injectiveness of Rational Functions |

Department | Department of Mathematics |

Supervisor | ASSOCIATE PROF. Danny Neftin |

Full Thesis text |

The most difficult open case of the Carney Hortsch Zieve
conjecture for curves is to show that for every number field* K*, there
exists a constant *N*, such that for any rational function f with
coefficients in K, the induces map *P ^{1}* (

Let *k *be the algebraic closure of the rational
numbers. Our main contribution is building on top of geometrically
indecomposable maps that induce a map which is at least *2-to-1* for
infinitely many valued in some number field. We show that if *f=f** _{2 }composed with f_{1} *induces a map that is
at least

We show that there exists a bound *N *depending only
on the number field *K,* such that for all new examples of functions *f*
that induce a map that is at least *2-to-1* for infinitely many values in *K, *the induces map *f: P ^{1}* (