L-function Lectures: PANTHers 2021

Professor Steven J Miller: sjm1@williams.edu

https://web.williams.edu/Mathematics/sjmiller/public_html/

Steven Miller: Williams College: Introduction for SMALL: Lecture

1. Introduction to the Zeta Function, Generating Function, Trace Formulas: https://youtu.be/ZN1QqEPl4LE (powerpoint here, pdf here)

2. Complex Analysis in an Hour: https://youtu.be/pvbdjcm5l8U (powerpoint here, pdf here)

3. Explicit Formulas, Prime Number Theorem: https://youtu.be/-Q9aoy62i8s (powerpoint here, pdf here)

4. Discussion on n-level correlations and n-level densities: https://youtu.be/kVgNLfnlIGA  (powerpoint here, pdf here)

5. Discussion of n-level densities for Dirichlet / Modular forms: https://youtu.be/Wj9iicvLw1w (powerpoint here, pdf here)

Useful talks:

L-Functions and Random Matrix Theory:

• Introductory lectures on Random Matrix Theory and L-functions:
  • Part I (Classical RMT, Intro L-fns, Dirichlet):            http://youtu.be/2PuUbk6gUMM (slides: part 1)
  • Part II (Convolving families, cusp forms: slides here): http://youtu.be/vJz6W24tDik       (slides part 2)
• From Sato-Tate Distributions to Low-Lying Zeros:  http://youtu.be/VBzVAvZ6k6A (slides here).
• From the Manhattan Project to Elliptic Curves: MASON IV (3/7/20). pdf  (video here: https://youtu.be/p15X3ERNvLs)
• Introduction to L-functions for SMALL students: 2021: https://web.williams.edu/Mathematics/sjmiller/public_html/math/talks/intronumbertheory/