Computational Number Theory - 1

Lecture course

This course will focus on analytic and arithmetic aspects of number theory.
The course will be taught in the Winter Semester of 2024-25 at the Max Planck Institute for Mathematics in the Sciences, Leipzig.
To audit the course online, please send me an email at kidambi[AT]duck[dot]com

Organizational details

All lectures will take place at the Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig.
Lectures will also be streamed via zoom, but not recorded.
Time and Location: Tuesdays (see below) E1 05 Leibniz Saal at 14:00
Any deviation from the course will be announced.
Kindly bring your laptops with you to the course. If you do not have a laptop, let me know.
Course Website

Software

You are free to choose any software/programming you like that you think you can use. I will be using Pari/GP. Installation instructions for Pari/GP.

Course schedule

Lecture 1, 25.10.2024, 11:00 (E2 10 (Leon Lichtenstein)): Introduction to computational number theory and Pari/GP
Lecture 2, 29.10.2024, 14:00 (E1 05 (Leibniz-Saal)): Introduction to Pari/GP
Lecture 3, 05.11.2024, 14:00 (E1 05 (Leibniz-Saal)): Computational al;gorithms for arithmetic Q
12.11.2024, 14:00 No lecture
19.11.2024: No lecture
Lecture 4, 26.11.2024: 14:00 (G3 10): Computational al;gorithms for arithmetic over Q
Lecture 5, 03.12.2024, 13:30 (G3 10): Quadratic reciprocity and characters
Lecture 6, 10.12.2024, 14:00 (G3 10): More on reciprocity and modular forms: Spaces of holomorphic modular forms
Lecture 7, 17.12.2024, 14:00 (G3 10): Dimensions of modular forms, q-series, and periods of modular forms
Lecture 8, 07.01.2025, 14:00 (G3 10): L-functions and coding session
Lecture 9, 14.01.2025, 13:30 (G3 10): L functions of elliptic curves and coding session
Lecture 10, 21.01.2025, 14:00 (G3 10): L-functions of K3 surfaces and coding session
Lecture 11, 28.01.2025, 14:00 (G3 10): L-functions of CY manifolds and motives and coding session
Lecture 12, 04.02.2025, 14:00 (G3 10): COmputing with motives, final lecture and projects

Update

You can find a calendar under Teaching.

Course Notes

Code Repository

You can also access the code from the following GitHub repository. To submit code to this repository (as a part of your homework), please request access from me.

Literature