Multiplicative Number Theory I: Classical Theory

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Cambridge University Press, Nov 16, 2006 - Mathematics
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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 most important unsolved problem in the mathematical world. Assuming only subjects covered in a standard degree in mathematics, the authors comprehensively cover all the topics met in first courses on multiplicative number theory and the distribution of prime numbers. They bring their extensive and distinguished research expertise to bear in preparing the student for intelligent reading of the more advanced research literature. This 2006 text, which is based on courses taught successfully over many years at Michigan, Imperial College and Pennsylvania State, is enriched by comprehensive historical notes and references as well as over 500 exercises.
  

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Contents

The gamma function
520
Topics in harmonic analysis
535
I
1
The elementary theory of arithmetic functions
35
Principles and first examples of sieve methods
76
I
108
II
137
The Prime Number Theorem
168
Primitive characters and Gauss sums
282
Analytic properties of the zeta function and Lfunctions
326
II
358
Explicit formulŠ
397
Conditional estimates
419
Zeros
452
Oscillations of error terms
463
Name index
544

Applications of the Prime Number Theorem
199
Further discussion of the Prime Number Theorem
244
APPENDICES
xi
Subject index 550
xix

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