MA 358: Topics in Number Theory 4 (p-adic L-functions)

Credits: 3:0

Pre-requisites :

1. a solid background in Algebraic Number Theory
2. some familiarity with elliptic curves and modular forms.
3. a good background in commutative algebra
4. some knowledge of L-functions (analytic number theory) will be preferable.

We plan to cover (possibly a subset of) the following topics:

1. Kubota—Leopoldt p-adic L-functions
2. P-adic measures
3. Leopoldt’s formula for L_p(1,chi)
4. P-adic L-functions of totally real fields (following Deligne—Ribet)
5. P-adic L-functions of ordinary elliptic curves and modular forms

Suggested books and references:

1. Koblitz, p-adic Numbers, p-adic Analysis, and Zeta-Functions
2. Iwasawa, Lectures on P-Adic L-Functions
3. Washington, Introduction to cyclotomic fields
4. Lang, Cyclotomic fields
5. Diamond--Shurman, A First Course in Modular Forms
6. Manin, Parabolic points and Zeta functions of modular curves
7. Deligne—Ribet, Values of abelian L-functions at negative integers over totally real fields

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