Advanced Topics in Analytic Number Theory

A.Y. 2017/2018
6
Max ECTS
42
Overall hours
SSD
MAT/05
Language
English
Learning objectives
Starting with the second half of the past century it became clear that the classical constructions in number theory associating L functions to several algebraic objects can be considered as special instances of a general Fourier theory on suitable abelian and locally compact groups. The course wishes to introduce this theory and clarify these connections.
Expected learning outcomes
Students will know the basic results of the Fourier analysis on abelian and locally compact groups.
Course syllabus and organization

Single session

Responsible
Lesson period
Second semester
Course syllabus
Locally compact groups, Haar measure.

Abelian locally compact groups, representations, spectral theorems and Pontryagin duality.

Classification of locally compact fields.

Applications to Adèle and Idèle groups.
MAT/05 - MATHEMATICAL ANALYSIS - University credits: 6
Lessons: 42 hours
Professor: Molteni Giuseppe
Professor(s)
Reception:
My office: Dipartimento di Matematica, via Saldini 50, first floor