In the spring term of 2020 (January - March), I gave a TCC course on p-adic L-functions and Iwasawa theory. 

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The first half of the course was a modified version of the London Taught Course Centre course I gave with Joaquín Rodrigues Jacinto in 2017, titled 'An introduction to p-adic L-functions'.

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Lecture notes

There are two sets of lecture notes, treating the two halves of the course. The first set covers the case of GL(1) - that is, the Riemann zeta function and Dirichlet L-functions - and was written jointly with Joaquín Rodrigues Jacinto. The second set covers the case of GL(2), that is, the case of modular forms and elliptic curves.

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• Lecture notes, Part I: p-adic L-functions for GL(1) and the Iwasawa main conjecture

• Lecture notes, Part II: p-adic L-functions for modular forms

 

Exercise sheets

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• Exercise sheet 1  - (The Kubota-Leopoldt p-adic L-function)

• Exercise sheet 2  - (Iwasawa main conjecture for GL(1))

• Exercise sheet 3  - (Modular forms and p-adic distributions)

• Bonus exercises  - (p-adic L-functions over number fields, Bernoulli distributions)