Lecture Notes:

• Lecture 1: Introduction
• Lecture 2: Chebyshev's estimates
• Lecture 3: Review of complex analysis
• Lecture 4: Perron's formula
• Lecture 5: Estimates for the Riemann zeta function and the PNT
• Further reading: Newman's short proof of the prime number theorem (D. Zagier)
• Lecture 6: The functional equation for the Riemann zeta function
• Lecture 7: Entire functions of finite order
• Arithmetic functions
• Average Orders
• Further reading: A useful bound
• Dirichlet Characters
• Dirichlet L-functions
• Gauss sums
• Incomplete character sums

Homework Problems:

• Problem sheet 1 (by 16th Feb)
• Problem sheet 2 (by 16th Mar)

Past Exams:

• 2013/2014
• 2014/2015
• 2015/2016

References:

• A. Booker and T. Browning, Lecture notes (2016)
• T.M. Apostol, Introduction to analytic number theory, Springer, 1976
• H. Davenport, Multiplicative Number Theory, third edition, Springer 2000
• H.L. Montgomery and R.C. Vaughan, Multiplicative Number Theory I. Classical Theory, Cambridge University Press 2007
• G. Tenebaum, Introduction to analytic and probabilistic number theory, Cambridge University Press, 1995