L-functions

Spring 2026, Jinan

Time and Place: 

Friday 10:00-12:00,  逸夫信息楼 A307.

Instructors: 

Bingrong Huang

Prerequisites:

Basic Analytic Number Theory and Automorphic Forms.

Syllabus:

This is a reading course. We plan to read the following papers in this semester.

[Li] 

Li, Xiannan.

Moments of quadratic twists of modular L-functions.

Invent. Math. 237 (2024), no. 2, 697–733.

[CLMR8] 

Chandee, Vorrapan; Li, Xiannan; Matomäki, Kaisa; Radziwiłł, Maksym.

The eighth moment of Dirichlet L-functions II.

Duke Math. J. 173 (2024), no. 18, 3453–3493.

[CLMR6] 

Chandee, Vorrapan; Li, Xiannan; Matomäki, Kaisa; Radziwiłł, Maksym.

The sixth moment of Dirichlet L-functions at the central point.

https://arxiv.org/abs/2409.01457.

Other references:

[IK] Chapter 5

Iwaniec, Henryk; Kowalski, Emmanuel.

Analytic number theory.

Amer. Math. Soc. Colloq. Publ., 53. American Mathematical Society, Providence, RI, 2004, xii+615 pp.

[BCdSGKK]

Bump, D.; Cogdell, J. W.; de Shalit, E.; Gaitsgory, D.; Kowalski, E.; Kudla, S. S.

An introduction to the Langlands program.

Lectures presented at the Hebrew University of Jerusalem, Jerusalem, March 12–16, 2001. Edited by Joseph Bernstein and Stephen Gelbart

Birkhäuser Boston, Inc., Boston, MA, 2003. x+281 pp.

[Sound]

Soundararajan, Kannan.

The distribution of values of zeta and L-functions.

ICM—International Congress of Mathematicians. Vol. 2. Plenary lectures, 1260–1310.

EMS Press, Berlin, [2023], ©2023

Schedule:

Date	Speaker	Title	References
March 06	Bingrong Huang	L-functions	Introduction
March 13			[Li]
March 20			[Li]
March 27			[Li]
April 03			[Li]
April 10			[CLMR8]
April 17			[CLMR8]
April 24			[CLMR8]
May 01	NO CLASS
May 08			[CLMR8]
May 15			[CLMR8]
May 22			[CLMR6]
May 29			[CLMR6]
June 05			[CLMR6]
June 12			[CLMR6]
June 19	NO CLASS
June 26			[CLMR6]

Contact: 

Bingrong Huang (Email: brhuang (AT) sdu.edu.cn; Office: Mingde Building C701)