Math 297 (Analytic number theory)

07 Aug 2019

• Euler's proof of the infinitude of the primes
• Euler product formula for the Riemann zeta function
• The sum of the reciprocal of the primes diverges
• Density of the squarefree integers

14 Aug 2019

• Arithmetic functions and examples (Möbius, Euler's totient, I, u, N)
• Dirichlet series and Dirichlet product
• Identities: μ * u = I, φ * u = N
• Dirichlet series of the Möbius function
• Möbius inversion formula
• Summatory functions
• Abel's identity

16 Aug 2019

• Euler's summation formula
• Big O notation
• Elementary asymptotic formulas
• Average order of d(n) and σ(n)