Course details
Semester
- Autumn 2021
- Monday, October 4th to Friday, December 10th
Hours
- Live lecture hours
- 10
- Recorded lecture hours
- 0
- Total advised study hours
- 40
Timetable
- Wednesdays
- 10:05 - 10:55 (UK)
Description
This course gives an introduction to the subject. Here is a sample of topics we plan to cover:
- Modular curves, also as Riemann surfaces and as moduli space of elliptic curves (over C);
- Modular functions and forms, basic properties, Eisenstein series, eta-function;
- Hecke operators, Petersson scalar product;
- Modular forms and Dirichlet series, functional equation;
- Theta series, arithmetic applications;
- "A First Course in Modular Forms" by Diamond and Shurman
- "Topics in Classical Automorphic Forms" by Iwaniec
- "Introduction to Elliptic Curves and Modular Forms" by Koblitz, and
- "Modular Forms" by Miyake
Prerequisites
Occasionally, some knowledge of algebraic number theory and Riemann surface theory would be helpful.
Syllabus
- Modular curves, also as Riemann surfaces and as moduli space of elliptic curves (over C)
- Modular functions and forms, basic properties, Eisenstein series, eta-function
- Theta series, arithmetic applications
- Modular forms and Dirichlet series, functional equation
- Hecke operators, Petersson scalar product
Lecturer
-
SM
Sacha Mangerel
- University
- Durham University
Bibliography
No bibliography has been specified for this course.
Assessment
The assessment for this course will be released on Sunday 9th January 2022 at 00:00 and is due in before Sunday 23rd January 2022 at 23:59.
Assessment for all MAGIC courses is via take-home exam which will be made available at the release date (the start of the exam period).
You will need to upload a PDF file with your own attempted solutions by the due date (the end of the exam period).
If you have kept up-to-date with the course, the expectation is it should take at most 3 hours’ work to attain the pass mark, which is 50%.
Please note that you are not registered for assessment on this course.
Files
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Lectures
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