Mathematics 207b

Number Theory

Elementary modular Iwasawa theory

Spring Quarter 2018

Haruzo HIDA

**Meeting Time:** Mondays, Wednesdays and Fridays 2:00pm to
2:50pm in MS 6201.

**Although this is a topic course,
the content is elementary and good for first year students.**

Here is a link to an overview of the course [pdf].

**Office hours:** Before the class meeting on Monday/Wednesday 1pm-1:50pm
at my office: MS6308.

## Lecture Starts on Monday April 2nd at 2pm in MS 6201

**Lecture notes:**

Notes (pdf file, a tentative version almost complete).

Grading will be based on student presentation either in the seminar course Math 290b.3.18s or in the class meeting at the end of courses on topics (close to the course material)
chosen by each student.
No final exam is planned.
As reference books,
we suggest

[EFN] S. Lang, Elliptic functions, Second edition, GTM **112**, 1987, Springer,br>
[MUN] D. Kubert and S. Lang, Modular units, Springer, GMW **244**, 1981, Springer,

[ELE] H. Hida, Elementary Theory of L-functions
and Eisenstein Series,
LMSST **26**, Cambridge University Press, Cambridge, 1993.
**Topics:** In this course, assuming basic knowledge
of complex analysis,
we describe basics of elliptic modular forms.
We hope to cover the following four topics:

Explicit construction of modular forms and modular functions;
Determination of units in the elliptic modular function fields (modular units);
The cuspidal class group of modular curves including a proof of the cuspidal class number formula.
If time allows, we go further as described in the overview.

**Prerequisite:**

Good understanding of commutative algebra, complex analysis and
algebraic number theory.