Modular forms

This is an undergraduate course on modular. Please read the course template for text-books and other important information about the course. This is the course MTH 434 and it is a 3 credit course.

Grading :

1. Mid-Semester Exams-30%
2. End-Semester Exams-30%.

3. Class tests (4):-10%+10%+10%+10%.

Please note that there will not be any repeat class tests.

Recommended Reading:

1. Diamond Shurman-A first course in modular forms. (Graduate text of mathematics).
2. Modular forms-Miyake.
3. Modular forms (a computational approach)-By William Stein.

Prerequisites: Complex analysis

Class timing:

Tue 2-2.55 pm

Wed-12-12.55 pm.

Class room

LHC 201

Week 1

1.6/8/2019 Lecture 1:-Weakly modular form for full congruence subgroups, examples, motivation.

2. 7/8/2019:Lecture 2 :holomorphic at infinity, modular forms, group actions.

Week 2

3. 13/8/2019: Lecture 3 -Fourier expansion of Eisenstein series.

4. 14/8/2019: Lecture 4. : Fundamental domain.

Week 3

4' Assignement 1

5. 20/8/2019: Lecture 5. Tutorial.

6. 21/8/2019: Class test 1.

Week 4

7. 27/8/2019:Valence formula.

8. 28/8/2019: Structure theorems for level one modular forms.

Week 5

9. 3/9/19: Congruence subgroup and topology of quotient spaces.

10. 4/9/19:Modular forms for congruence subgroups.

Week 6

11.10/9/2019:-Muharam (holiday).

12. 11/9/2019:-Tutorial.

Week 7

13. 17/9/2019:-No class; please prepare for Mid-Sem exam.

14. 18/09/2019:-Class test 2.

Week 8

Mid-sem:

Mid-sem exam 26/9/19 at 3-5 pm.

Week 9:-

18. 1/10/2019 :-Petersson inner products.

19. 2/10/2019: Gandhi Jayanti

Week 10

20. 8/10/2019: Dusherra

21. 9/10/2019:-No class; puja vacation

22. 11/10/2019:-Petersson inner product (revision).

Week 11:-

23. 15/10/2019- Hecke operators

24. 16/10/2019:-Explicit description of sublattices and Hecke operators on Fourier expansion.

Week 12:-

26. 22/10/2019 :- Tutorial.

27. 23/10/2019 :- Tutorial

Class test 3 (Date to be announced).

Week 13:-

29/10/2019:-Hecke operators for congruence subgroups. (Double coset operators).

30/10/2019:-Diamonds and T_p operators

31/10/2019: Class test 3

Week 14:-

5/11/2019:- Fourier expansion of T_p operators.

6/11/2019:-Eigenforms, new and old forms.

Week 15:-

12/11/2019:-Holiday

13/11/2019:-Class test 4

Week 15:-

19/11/2019:--L-functions of modular forms

20/11/2019: Hecke operators are self adjoint (proof using Poincare series), Tutorial, Online demonstation using SAGE.

Week 16:-

24. (25/11/2019):- End-semester examination.