# Nic Fellini (Queen's University)

Date

Monday January 22, 20243:00 pm - 4:00 pm

Location

Jeffery Hall, Room 319Event Category

## Number Theory Seminar

**Monday, January 22nd, 2024**

**Time:** 3:00 p.m. **Place:** Jeffery Hall, Room 319

**Speaker:** Nic Fellini (Queen's University)

**Title:** Reflections on the congruence relations of Ankeny, Artin, and Chowla

**Abstract:** In 1951, Ankeny, Artin, and Chowla released a short note containing four congruence relations involving the arithmetic invariants of \Q(\sqrt{d}) for d\equiv 1 \bmod{4}. The following year, Ankeny, Artin, and Chowla proved three of the four congruences from their earlier note using p-adic methods. Using p-adic L-functions we will give a cohesive explanation of these congruences as well as a new proof of the originally omitted congruence.