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Analytic Number Theory - MAT00051M

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  • Department: Mathematics
  • Module co-ordinator: Prof. Sanju Velani
  • Credit value: 10 credits
  • Credit level: M
  • Academic year of delivery: 2017-18

Module will run

Occurrence Teaching cycle
A Spring Term 2017-18

Module aims

The aim of the module is to show how analytic properties of the Riemann zeta function imply results on prime numbers.

Module learning outcomes

At the end of the module you should be able to:

Understand arithmetic applications of Dirichlet series.

Know analytic aspects of the Riemann zeta function (functional equation, analytic continuation).

Appreciate the connection between zeros of the Riemann zeta function and properties of prime numbers.

Know the prime number theorem.

Know how Dirichlet L-functions help us understand primes in arithmetic progressions.


Task Length % of module mark
University - closed examination
Analytic Number Theory
2 hours 100

Special assessment rules



Task Length % of module mark
University - closed examination
Analytic Number Theory
2 hours 100

Module feedback

Information currently unavailable

Indicative reading

Recent Perspectives in Random Matrix Theory and Number Theory (Mezzadri and Snaith eds) LMS Lecture Notes Series 322, ISBN 0-521-62058-9 (S 2.81 MEZ)

An Invitation to Modern Number Theory, (Miller and Takloo-Bighash) ISBN: 0-691-12060-9 (S 2.81 MIL)

Riemann's Zeta Function (Edwards) ISBN 0-486-41740-9 (S 7.36 EDW)

Analytic number theory (Iwaniec and Kowalski) ISBN 0-821-83633-1 (S 2.81 IWA)

Multiplicative number theory I : classical theory (Montgomery and Vaughan) ISBN 0-521-84903-9 (S 2.814 MON)

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.