# MMA340, Analytic Number Theory, Spring 19

## Latest news

Welcome to the course! The schedule for the course can be found in TimeEdit.

2019-03-13: The final homework assignment has been graded. You can pick up your solutions in my office on Friday March 15.

2019-02-28: The third homework assignment is now available below.

2019-02-18: The formulation of Problem 1b of Assignment 2 has been updated.

2019-02-14: The second homework assignment is now available below.

2019-02-04: There was a mistake in the formulation of problem 2b of Assignment 1. The text has now been updated.

2019-01-31: The first homework assignment is now available below.

## Teachers

Course coordinator: Anders Södergren, office L3081, e-mail: andesod(at)chalmers(dot)se

## Course literature

H. Davenport, Multiplicative number theory, third edition, Springer-Verlag, 2000.

Complementary reading in Elementary Number Theory:
I. Niven, H. S. Zuckerman, H. L. Montgomery, An introduction to the theory of numbers, fifth edition, John Wiley & Sons, 1991.

## Program

#### Lectures

Day
Sections Contents
Monday 21/1

Short introduction. Arithmetic functions.
Wednesday 23/1

Arithmetic functions
Friday 25/1

Arithmetic functions
Monday 28/1

Arithmetic functions
Wednesday 30/1

Elementary results on prime counting
Friday 1/2
Elementary results on prime counting
Monday 4/2 7
Elementary results on prime counting
Wednesday 6/2 1,8
Dirichlet series
Friday 8/2 1,8
Dirichlet series
Monday 11/2
Dirichlet series and Euler products
Wednesday 13/2
Dirichlet series and Euler products
Friday 15/2
The Riemann zeta function
Monday 18/2 17-18
The prime number theorem
Wednesday 20/2 17-18
The prime number theorem
Friday 22/2 8-10
The Riemann zeta function
Monday 25/2 11-13
The Riemann zeta function
Wednesday 27/2 15,17,18
The prime number theorem
Friday 1/3
Dirichlet characters and Dirichlet L-functions
Monday 4/3
Dirichlet characters and Dirichlet L-functions
Wednesday 6/3 1,4
The prime number theorem in arithmetic progressions
Friday 8/3 14,20
The prime number theorem in arithmetic progressions

#### Recommended exercises

Week
Exercises
1 Exercise sheet 1
2 Exercise sheet 2
3 Exercise sheet 3
4 Exercise sheet 4
5 Exercise sheet 5
6 Exercise sheet 6
7 Exercise sheet 7

## Course requirements

The learning goals of the course can be found in the course plan.

## Assignments

There will be three sets of homework assignments distributed during the course. Each set will consist of 3-5 problems.

Assignment 1

Assignment 2

Assignment 3

NOTE: The following is to clarify the rules for everybody interested in working with these assignments. You are free to cooperate with other students and to read whatever literature you can find about the subject. However, you are expected to formulate your solutions independently and it is neither allowed to copy from other students nor to copy solutions form any other source! No credit will be given to such solutions and if this happens in a systematic fashion you will be reported for plagiarism.

## Examination

The examination consists of written homework assignments and an oral examination at the end of the course.

To pass the course you are required to solve at least 50% of the homework assignments and to pass the oral exam.

At the time of the exam you are supposed to know all the definitions and theorems (including proofs) that are from the relevant sections of the course literature or done in class. You are also supposed to be able to apply the methods and results of the course to analyze examples, solve problems and prove theorems.

## Examination procedures

In Chalmers Student Portal you can read about when exams are given and what rules apply on exams at Chalmers. In addition to that, there is a schedule when exams are given for courses at University of Gothenburg.

Before the exam, it is important that you sign up for the examination. If you study at Chalmers, you will do this by the Chalmers Student Portal, and if you study at University of Gothenburg, you sign up via GU's Student Portal, where you also can read about what rules apply to examination at University of Gothenburg.

At the exam, you should be able to show valid identification.