Mathematics 205B

Topics in Number Theory

Modular forms and their Galois representations.

Winter Quarter 2017

Haruzo HIDA

Meeting Time: Regularly Mondays and Wednesdays 2:00 pm to 2:50 pm in MS 5148 and Fridays either 2:00 pm to 2:50pm or 4:00 pm to 5:30 pm in MS 5148 (Friday meeting time will be announced in the class before the meeting day).

Lecture Starts on Monday January 9th in MS 5148

Office hours: Before class meetings, from 1:00pm (MW) at my office: MS6308.

Texts: Tentative lecture notes has been posted:
Version of 3/3/17: Notes (pdf file).
An old lecture notes on elliptic curves and modular forms (describes how to compute the equation of a given elliptic curve):
Notes no.2 (pdf file)

Grading will be based on student presentation in the last week of teaching (or in the student participating seminar). No final exam is planned.

As reference books, we list
[LFE]:"Elementary Theory of L-functions and Eisenstein Series," LMSST 26, Cambridge University Press, Cambridge, 1993, Chapters 5, 7
[GME]:"Geometric Modular Forms and Elliptic Curves," (World Scientific) First (2000) or Second edition (2011), Chapters 1, 2 and 4
[ALR]: Serre's book: "Abelian l-Adic Representations and Elliptic Curves," any edition, for example, Research Notes in Mathematics 7, A K Peters, 1998

Topics: I would touch the following topics in this course:

If we do not reach the last item within this quarter, we continue to go in this line in the Spring quarter 2017. If we finish the objectives listed here within this quarter, Spring 2017 course will cover slightly more advanced topics.

In addition to above four topics,

Good understanding of the material covered by Math 210 series (including commutative and non-commutative algebra theory) and algebraic number theory.