Multiplicative number theory I classical theory
Prime numbers are the multiplicative building blocks of natural numbers. Understanding their overall influence and especially their distribution gives rise to central questions in mathematics and physics. In particular their finer distribution is closely connected with the Riemann hypothesis, the mo...
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge
Cambridge University Press
2007
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| Schriftenreihe: | Cambridge studies in advanced mathematics
97 |
| Schlagworte: | |
| Online-Zugang: | DE-12 DE-92 DE-355 URL des Erstveröffentlichers |
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Inhaltsangabe:
- 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