p-adic L-functions for modular forms

Lecture notes:  notes can be found here (last updated: 29th April 2026)

Course description: P-adic L-functions are important objects in the arithmetic of modular forms which encode interesting information about congruences between special values of their complex L-functions modulo powers of p. In the first half of this course, we will cover the construction of these p-adic L-functions via the machinery of overconvergent modular symbols. The second half will then focus on further topics, including the exceptional zero formula of Greenberg and Stevens and the connection with Galois representations. Prerequisites: familiarity with modular forms (a first course is sufficient), p-adic numbers, and Galois theory.

Topics to be covered include:

• Modular forms and their L-functions

• Modular symbols

• Overconvergent modular symbols and p-adic families

• P-adic measures and distributions

• L-invariants and the exceptional zero formula

• Galois representations attached to modular forms

When: Wednesdays, 14:00 - 16:00 (No lecture on Weds 13 May)