# Emmanuel Kowalski: Catalogue data in Spring Semester 2021

Name | Prof. Dr. Emmanuel Kowalski |

Field | Mathematics |

Address | Professur für Mathematik ETH Zürich, HG G 64.1 Rämistrasse 101 8092 Zürich SWITZERLAND |

Telephone | +41 44 632 34 41 |

emmanuel.kowalski@math.ethz.ch | |

URL | http://www.math.ethz.ch/~kowalski |

Department | Mathematics |

Relationship | Full Professor |

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

401-3109-65L | Probabilistic Number Theory | 8 credits | 4G | E. Kowalski | |

Abstract | The course presents some results of probabilistic number theory in a unified manner, including distribution properties of the number of prime divisors of integers, probabilistic properties of the zeta function and statistical distribution of exponential sums. | ||||

Objective | The goal of the course is to present some results of probabilistic number theory in a unified manner. | ||||

Content | The main concepts will be presented in parallel with the proof of a few main theorems: (1) the Erdős-Wintner and Erdős-Kac theorems concerning the distribution of values of arithmetic functions; (2) the distribution of values of the Riemann zeta function, including Selberg's central limit theorem for the Riemann zeta function on the critical line; (3) the Chebychev bias for primes in arithmetic progressions; (4) functional limit theorems for the paths of partial sums of families of exponential sums. | ||||

Lecture notes | The lecture notes for the class are available at https://www.math.ethz.ch/~kowalski/probabilistic-number-theory.pdf | ||||

Prerequisites / Notice | Prerequisites: Complex analysis, measure and integral, and at least the basic language of probability theory (the main concepts, such as convergence in law, will be recalled). Some knowledge of number theory is useful but the main results will also be summarized. | ||||

401-5110-00L | Number Theory Seminar | 0 credits | 1K | Ö. Imamoglu, P. S. Jossen, E. Kowalski, P. D. Nelson, R. Pink, G. Wüstholz | |

Abstract | Research colloquium | ||||

Objective | Talks on various topics of current research. | ||||

Content | Research seminar in algebra, number theory and geometry. This seminar is aimed in particular to members of the research groups in these areas and their graduate students. |