# 401-3117-66L Introduction to the Circle Method

Semester | Autumn Semester 2016 |

Lecturers | E. Kowalski |

Periodicity | non-recurring course |

Language of instruction | English |

### Catalogue data

Abstract | The circle method, invented by Hardy and Ramanujan and developped by Hardy and Littlewood and Kloosterman, is one of the most versatile methods currently available to determine the asymptotic behavior of the number of integral solutions to polynomial equations, when the number of solutions is sufficiently large. |

Objective | |

Content | The circle method, invented by Hardy and Ramanujan and developped by Hardy and Littlewood and Kloosterman, is one of the most versatile methods currently available to determine the asymptotic behavior of the number of integral solutions to polynomial equations, when the number of solutions is sufficiently large. The lecture will present an introduction to this method. In particular, it will present the solution of Waring's Problem concerning the representability of integers as sums of a bounded numbers of (fixed) powers of integers. |

Literature | H. Davenport, "Analytic methods for Diophantine equations and Diophatine inequalities", Cambridge H. Iwaniec and E. Kowalski, "Analytic number theory", chapter 20; AMS R. Vaughan, "The Hardy-Littlewood method", Cambridge |

### Performance assessment

Performance assessment information (valid until the course unit is held again) | |

Performance assessment as a semester course | |

ECTS credits | 6 credits |

Examiners | E. Kowalski |

Type | session examination |

Language of examination | English |

Repetition | The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit. |

Mode of examination | oral 20 minutes |

This information can be updated until the beginning of the semester; information on the examination timetable is binding. |

### Learning materials

No public learning materials available. | |

Only public learning materials are listed. |

### Courses

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

401-3117-66 V | Introduction to the Circle Method | 2 hrs |
| E. Kowalski | ||||||

401-3117-66 U | Introduction to the Circle Method NOTICE: on November 25, 2016 the exercises take place in HG F 26.1 | 1 hrs |
| E. Kowalski |

### Groups

No information on groups available. |

### Restrictions

There are no additional restrictions for the registration. |

### Offered in

Programme | Section | Type | |
---|---|---|---|

Mathematics Bachelor | Selection: Algebra, Topology, Discrete Mathematics, Logic | W | |

Mathematics Master | Selection: Algebra, Topology, Discrete Mathematics, Logic | W |