Description

Book Synopsis
The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.

Table of Contents
  • Introduction.
  • Dessins d'enfants: From polynomials through Belyi functions to weighted trees.
  • Existence theorem.
  • Recapitulation and perspective.
  • Classification of unitrees.
  • Computation of Davenport-Zannier pairs for unitrees.
  • Primitive monodromy groups of weighted trees.
  • Trees with primitive monodromy groups.
  • A zoo of examples and constructions.
  • Diophantine invariants.
  • Enumeration.
  • What remains to be done.
  • Bibliography.
  • Index.

DavenportZannier Polynomials and Dessins dEnfants

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    A Paperback / softback by Nikolai M. Adrianov, Fedor Pakovich, Alexander K. Zvonkin

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      View other formats and editions of DavenportZannier Polynomials and Dessins dEnfants by Nikolai M. Adrianov

      Publisher: American Mathematical Society
      Publication Date: 30/09/2020
      ISBN13: 9781470456344, 978-1470456344
      ISBN10: 1470456346
      Also in:
      Combinatorics and graph theory Number theory

      Description

      Book Synopsis
      The polynomials studied in this book take their origin in number theory. The authors show how, by drawing simple pictures, one can prove some long-standing conjectures and formulate new ones. The theory presented here touches upon many different fields of mathematics.

      Table of Contents
      • Introduction.
      • Dessins d'enfants: From polynomials through Belyi functions to weighted trees.
      • Existence theorem.
      • Recapitulation and perspective.
      • Classification of unitrees.
      • Computation of Davenport-Zannier pairs for unitrees.
      • Primitive monodromy groups of weighted trees.
      • Trees with primitive monodromy groups.
      • A zoo of examples and constructions.
      • Diophantine invariants.
      • Enumeration.
      • What remains to be done.
      • Bibliography.
      • Index.

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