This is an introduction to analytic number theory developed through the study of the distribution of prime numbers, highlighting how analytic number theorists think. The central focus is on the Prime Number Theorem, presented through a proof selected to balance conceptual understanding with technical depth, alongside a sketch of Riemann's classical approach to highlight the subject's elegance. Providing a wide range of further directions (e.g., sieve methods, the anatomy of integers, primes in arithmetic progressions, prime gaps, smooth numbers, and extensive discussion of probabilistic heuristics which play an important role in guiding research goals), the emphasis throughout the book is on clarity of argument and the development of technique using a conversational style of writing. The book ends with 13 short introductions to hot topics. The book assumes familiarity with elementary number theory and basic complex analysis, though it provides helpful review material. Boxed equations highlight the most memorable formulas; exercises, some embedded directly in the proofs, are designed to deepen understanding without becoming overwhelming. Its flexible structure makes the book suitable for various course designs, whether emphasizing core theory or incorporating optional sections on combinatorics, arithmetic progressions, or open research problems. By blending classical results with current perspectives, this book prepares advanced undergraduates and beginning graduate students to not just learn analytic number theory, but to acquire contemporary ways of thinking about the subject.
- 293 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
About this book
Information
Subtopic
Mathematics GeneralIndex
MathematicsTable of contents
- Cover
- Title page
- Preface
- Definitions
- Part 1. Background in analytic number theory
- Part 2. Anatomies of mathematical objects
- Part 3. Sieves and primes
- Part 4. Background in analysis
- Part 5. The proof of the Prime Number Theorem
- Part 6. Primes in arithmetic progressions
- Part 7. A dozen and one different directions
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Yes, you can access Analytic Number Theory Revealed by Andrew Granville in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over 1.5 million books available in our catalogue for you to explore.