Course notes
Mathematical Institute
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ANALYTIC NUMBER THEORY: PRIME NUMBER THEORY
Chapter 0: Notation and prerequisites
Chapter 1: Introduction to prime number theory
Chapter 2: Dirichlet series and arithmetic functions
Chapter 3: Characters and Gauss sums
Chapter 4: The Riemann zeta function and L-functions
Chapter 5: Tauberian theorems
Chapter 6: The Prime Number Theorem for arithmetic progressions
DIOPHANTINE APPROXIMATION
Chapter 1: Introduction
Chapter 2: Geometry of numbers
Chapter 3: Algebraic numbers and algebraic number fields
Chapter 4: Transcendence results
Chapter 5: Linear forms in logarithms
Chapter 6: Approximation to algebraic numbers by rationals
Chapter 7: The Subspace Theorem
Chapter 8: The p-adic Subspace Theorem
OTHER COURSE NOTES
P-adic numbers and linear recurrence sequences