Fundamentals in Number Theory

Spring 2023

Schedule: Tuesday 14：00-15：50，Friday 10：10-12：00.

Classroom: 董明珠楼211d.

Syllabus:

The purpose of this course is to introduce some classic topics in analytic and algebraic number theory. The topics include:

1. Arithmetic functions.

2. Elementary results on the distribution of prime numbers with applications and related results. 

3. The Riemann zeta-function.

4. Analytic proof of the prime number theorem.

5. p-adic fields and the local-global principle of quadratic forms.

Bibliography:

[I] H. Iwaniec, Lectures on the Riemann Zeta Function.

[IF] H. Iwaniec and E. Kowalski, Analytic Number Theory.

[P] 潘承洞，《数论基础》.

[S] J.-P. Serre, A Course in Arithmetic.

[T] G. Tenenbaum, Introduction to Analytic and Probabilistic Number Theory.

Lecture Notes:

Lecture 1.pdf 2.24

Lecture 2.pdf 2.28 & 3.3

Lecture 3.pdf 3.7 & 3.10

Lecture 4.pdf 3.14 & 3.17

Lecture 5.pdf 3.21 & 3.24

Lecture 6.pdf 3.28

Lecture 7.pdf 4.4 

Lecture 8.pdf 4.7 & 4.11

Lecture 9.pdf 4.14 (Hand-written version, will later be replaced by a printed version) 

Homeworks:

2023Homework1.pdf due 2023.3.10

2023Homework2.pdf due 2023.3.17

2023Homework3.pdf due 2023.3.31

2023Homework4.pdf due 2023.4.7

2023Homework5.pdf due 2023.4.14

2023Homework6.pdf due 2023.4.25

2023Homework7.pdf due 2023.5.5

Contact: Ke Wang, ke_wang@sdu.edu.cn. Office: 明德楼C706.