Additive Number Theory

This is the webpage for my Part III course on Additive Number Theory, which was given in Lent Term 2007. A schedule for the course may be found here.

Notes on the exam: there will be a section A and a section B. You must answer one question from section A and two from section B. Section A will be on the first eight lectures of the course and section B on the last sixteen.

Big-O
The Big-O notation

Chapter 1
The prime number theorem [8 lectures]

Chapter 2
Sieve Theory [3 lectures]

Chapter 3
The Hardy-Littlewood Method

Important note: there was a serious error in Chapter 4 of the course, as lectured. The fourth displayed equation on page 72 does not follow trivially from Parseval's identity as claimed. The paper of Mauduit and Rivat is rather more complicated than the approach taken in the course, and now I understand why. As a result of this error section 4.5 of the course is now non-examinable.

Chapter 4 (lectured version, examinable except as stated above)
Binary digits of primes

Chapter 4 (corrected version for interested students, not examinable)

Appendix A
Fourier analysis

Appendix B
A primer on the Gamma function

Examples 1
Example Sheet 1

Examples 2
Example Sheet 2

Big-O The Big-O notation
Chapter 1 The prime number theorem [8 lectures]
Chapter 2 Sieve Theory [3 lectures]
Chapter 3 The Hardy-Littlewood Method
Important note: there was a serious error in Chapter 4 of the course, as lectured. The fourth displayed equation on page 72 does not follow trivially from Parseval's identity as claimed. The paper of Mauduit and Rivat is rather more complicated than the approach taken in the course, and now I understand why. As a result of this error section 4.5 of the course is now non-examinable.
Chapter 4 (lectured version, examinable except as stated above) Binary digits of primes
Chapter 4 (corrected version for interested students, not examinable)
Appendix A Fourier analysis
Appendix B A primer on the Gamma function
Examples 1 Example Sheet 1
Examples 2 Example Sheet 2