@phdthesis{Moeller2009,
  author    = {M{\"o}ller, Florian},
  title     = {Exceptional polynomials and monodromy groups in positive characteristic},
  url       = {http://nbn-resolving.de/urn:nbn:de:bvb:20-opus-34871},
  school      = {Universit{\"a}t W{\"u}rzburg},
  year      = {2009},
  abstract  = {We discuss exceptional polynomials, i.e. polynomials over a finite field \$k\$ that induce bijections over infinitely many finite extensions of \$k\$. In the first chapters we give the theoretical background to characterize this class of polynomials with Galois theoretic means. This leads to the notion of arithmetic resp. geometric monodromy groups. In the remaining chapters we restrict our attention to polynomials with primitive affine arithmetic monodromy group. We first classify all exceptional polynomials with the fixed field of the affine kernel of the arithmetic monodromy group being of genus less or equal to 2. Next we show that every full affine group can be realized as the monodromy group of a polynomial. In the remaining chapters we classify affine polynomials of a given degree.},
  subject      = {Algebraischer Funktionenk{\"o}rper},
  language  = {en}
}