Multiplicative number theory I : classical theory [E-Book] / Hugh L. Montgomery, Robert C. Vaughn.
Montgomery, Hugh L., (author)
Vaughan, R. C., (author)
Cambridge : Cambridge University Press, 2007
1 online resource (xvii, 552 pages)
Cambridge studies in advanced mathematics ; 97
Full Text
Table of Contents:
  • Dirichlet series I
  • The elementary theory of arithmetic functions
  • Principles and first examples of sieve methods
  • Primes in arithmetic progressions I
  • Dirichlet series II
  • The prime number theorem
  • Applications of the prime number theorem
  • Further discussion of the prime number theorem
  • Primitive characters and Gauss sums
  • Analytic properties of the zeta function and L-functions
  • Primes in arithmetic progressions II
  • Explicit formulae
  • Conditional estimates
  • Zeros
  • Oscillations of error terms
  • Appendices. A. The Riemann-Stieltjes integral; B. Bernoulli numbers and the Euler-MacLaurin summation formula; C. The gamma function; D. Topics in harmonic analysis.