Advanced arguments in analytic number theory 2017/'18
Lecturer prof. G. Molteni
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. The course is addressed to students in Mathematics at least in their third year degree with a basic knowledge of measure theory and of algebraic number fields. The course touches four main general topics:
| Programme | |
| Topic 1: | Locally compact groups, Haar measure. |
| Topic 2: | Abelian locally compact groups, representations, spectral theorems and Pontryagin duality. |
| Topic 3: | Classification of locally compact fields. |
| Topic 4: | Applications to Adèle and Idèle groups. |
| Bibliography | |
| D. Ramakrishnan, R. J. Valenza: Fourier Analysis on number fields, Graduate Texts in Mathematics 186, Springer, New-York, 1998. | |
| E. Hewitt, K. A. Ross: Abstract harmonic analysis volume I: Structure of topological groups, integration theory, group representations, Grundlehren der Mathematischen Wissenschaften, Springer--Verlag, Berlin-New York, 1979. | |
| E. Hewitt, K. A. Ross: Abstract harmonic analysis volume II: Structure and analysis for compact groups, analysis on locally compact abelian groups, Grundlehren der Mathematischen Wissenschaften, Springer--Verlag, Berlin-New York, 1970. |
Lectures
| Monday | 14.30-16.30 | Room 5 |
| Friday | 13.30-15.30 | Room 5 |
First lesson: Friday 2, March 2018!
Exam sessions
- to be scheduled
This work is licensed under a Creative Commons License.
Responsabile del sito: Giuseppe Molteni
Ultima modifica:
Ultima modifica: