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MA 358: Topics in Number Theory 4 (p-adic L-functions)
Credits: 3:0
Pre-requisites :
a solid background in Algebraic Number Theory
some familiarity with elliptic curves and modular forms.
a good background in commutative algebra
some knowledge of L-functions (analytic number theory) will be preferable.
We plan to cover (possibly a subset of) the following topics:
Kubota—Leopoldt p-adic L-functions
P-adic measures
Leopoldt’s formula for L_p(1,chi)
P-adic L-functions of totally real fields (following Deligne—Ribet)
P-adic L-functions of ordinary elliptic curves and modular forms
Suggested books and references:
Koblitz,
p-adic Numbers, p-adic Analysis, and Zeta-Functions
Iwasawa,
Lectures on P-Adic L-Functions
Washington,
Introduction to cyclotomic fields
Lang,
Cyclotomic fields
Diamond--Shurman,
A First Course in Modular Forms
Manin,
Parabolic points and Zeta functions of modular curves
Deligne—Ribet,
Values of abelian L-functions at negative integers over totally real fields
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Contact
:
+91 (80) 2293 2711, +91 (80) 2293 2265 ;
E-mail:
chair.math[at]iisc[dot]ac[dot]in
Last updated: 22 Sep 2023