NFMV026 Number theory in functions fields

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This page contains the program of the course. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

Program

The schedule of the course is in TimeEdit.

Note that changes might occur in the program.

In the table below the section numbers refer to sections in Rosen's book Number theory in function fields.

Lectures

Day Sections Content
Monday 20/3 Introduction to the course
Week 1 1-2 Background and motivation 
Week 2 3-4 Zeta functions, L-functions and primes in arithmetic progressions
Week 3 5 Zeta functions over Fq[T]
Week 4 5 Applications of the Riemann-Roch theorem 
Week 5 Appendix The Riemann Hypothesis
Week 6 6 The Riemann-Roch theorem
Week 7 7

The Riemann-Hurwitz theorem
Week 8 Primes in short intervals

 

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Recommended exercises

Week Exercises
1 Choose problems from Rosen's chapter 1, including problems 2-5 and 8.
2 Choose problems from Rosen's chapter 2, including problems 1-8 and 14-16.
3

Choose problems from Rosen's chapter 3, including problems 7 and 9, and chapter 4, including problems 2-5.
4 Exercises on divisors
5 Exercises on (and around) the Riemann Hypothesis
6 Exercises on adeles etc.
7 Computing the genus
8

 

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Assignments

There will be two sets of homework assignments distributed during the course. 

Assignment 1

Assignment 2

 

 

Course summary:

Course Summary
Date Details Due