## Paloma Bengoechea Duro: Catalogue data in Autumn Semester 2020 |

Name | Dr. Paloma Bengoechea Duro |

Department | Mathematics |

Relationship | Lecturer |

Number | Title | ECTS | Hours | Lecturers | |
---|---|---|---|---|---|

401-3119-70L | p-Adic Numbers | 4 credits | 2V | P. Bengoechea Duro | |

Abstract | This course is an introduction to the p-adic numbers. We will see how the field of p-adic numbers Q_p is build. We will explore the (strange) topology and the arithmetic of Q_p, as well as some elementary analytic concepts such as functions, continuity, integrals, etc. We will explain an algebraic and an analytic reasons of interest for the existence of p-adic numbers. | ||||

Objective | |||||

Content | - Absolute values on Q and Completions - Topology and Arithmetic of Q_p, p-adic Integers - Equations over p-adic numbers and Hensel's Lemma - Local-global principle - Hasse-Minkowski's Theorem on binary quadratic forms - Elementary Analysis in Q_p - the p-adic Riemann zeta function | ||||

Literature | "p-adic Numbers. An Introduction", Fernando Q. Gouvea (Springer) "p-adic Numbers, p-adic Analysis, and Zeta-Functions", Neal Koblitz (Springer) "p-adic numbers and Diophantine equations", Yuri Bilu (online notes 2013) | ||||

Prerequisites / Notice | The courses Topology, Measure and Integration, Algebra I/II are required prerequisites. |