MATH 649 : Learning seminar on L-functions
Leader: Rob Harron
Fall 2016
Lectures: W 10:30am–11:30am
Keller 314
Leader: Rob Harron
Fall 2016
Lectures: W 10:30am–11:30am
Keller 314
- The goal of this seminar is for the students to learn about L-functions (and zeta functions) in number theory and the objects they help us study. For the most part, students will be giving the lectures while I will be steering the way. All are invited to attend.
- L-functions play a central role in number theory these days. For instance, they are the subject of both the Riemann Hypothesis and the Birch and Swinnerton-Dyer Conjecture, and are a key part of the Langlands Programme (and arguably what the Langlands Programme is about). So, along the way, we will be introducing objects such as Dirichlet characters, number fields, elliptic curves, modular forms, and possibly automorphic representations and algebraic varieties.
Lecture schedule:
| Lecture 1 | Introduction/survey |
Rob Harron |
| Lecture 2 | Dirichlet characters, Dirichlet L-functions, and Dirichlet series (Part 1) | Dan Flores |
| Lecture 3 | Dirichlet characters, Dirichlet L-functions, and Dirichlet series (Part 2) | Dan Flores |
| Lecture 4 | Dirchlet's theorem on primes in arithmetic progressions, special values and functional equation of Dirichlet L-functions (Part 1) | Rob Harron |
| Lecture 5 | Dirchlet's theorem on primes in arithmetic progressions, special values and functional equation of Dirichlet L-functions (Part 2) | Rob Harron |
| Lecture 6 | Number fields and Dedekind zeta functions (Part 1) | Allan Wong |
| Lecture 7 | Number fields and Dedekind zeta functions (Part 2) | Allan Wong |
| Lecture ?? | Elliptic curves and their Hasse–Weil L-functions (Part 1) | Sarah Berner |
| Lecture ??+1 | Elliptic curves and their Hasse–Weil L-functions (Part 2) | Sarah Berner |
| Lecture ??? | Modular forms and their L-functions (Part 1) | Erik Holmes |
| Lecture ???+1 | Modular forms and their L-functions (Part 2) | Erik Holmes |
| Lecture ???? | Hecke's Grossencharacters and their L-functions (Part 1) | Jamal Hassan |
| Lecture ????+1 | Hecke's Grossencharacters and their L-functions (Part 2) | Jamal Hassan |
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