Introduction to Algebraic Number Theory

2024/2025

Учебный год

ENG

Обучение ведется на английском языке

6

Кредиты

Кто читает:

Факультет математики

Статус:

Дисциплина общефакультетского пула

Когда читается:

1, 2 модуль

Преподаватель

Жгун Владимир Сергеевич

Course Syllabus

Abstract

Many classical and modern problems in number theory can be interpreted in terms of properties of algebraic objects such as algebraic number fields, their rings of integers and orders in these rings, ideal class groups and unit groups. In this course, we will explore the main notions of algebraic number theory and connect them to some of the most classical problems and theorems, for example, the Dirichlet theorem on primes in arithmetic progressions, Gauss class number problem and Fermat’s last theorem. We will also learn about the properties of analytic and topological objects corresponding to number fields, such as the Dedekind zeta-function and the ring of adeles.