Number Theory

Analytic Number Theory

• Fundamentals of asymptotic analysis
  • Asymptotic notations
  • Euler's summation formula
  • Riemann zeta function
  • Abel's identity
  • Faulhaber's formula and Bernoulli numbers
• (WIP) Prime number theorem
  • Prime distribution functions
  • Selberg and Erdos's elementary proof
  • Applications of prime number theorem
• (WIP) Application: Improving prime number sieves