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Mastering Number Theory: Analytic Number Theory I: Prime‐Counting and the Riemann Zeta Function by Alexei Nowakowski

Mastering Number Theory: Analytic Number Theory I: Prime‐Counting and the Riemann Zeta Function

by Alexei Nowakowski
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Book cover type: Paperback
  • ISBN13: 9798282199734
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Publication Date:
  • Pages: 306
  • Original Price: GBP 22.57
  • Language: English
  • Edition: N/A
  • Item Weight: 413 grams
  • BISAC Subject(s): Number Theory

Warning: counting primes may induce an irrational obsession-fortunately, unlike π, your sanity here is well within finite bounds.

Prepare to dive headlong into a realm where every prime tells a story, every zero has its moment under the spotlight, and Python code is your trusty sidekick. Penned by an eccentric Math PhD who respects no wall of chalk dust, this textbook-with full Python demos-guides you through:

- Foundations of π(x), θ(x), ψ(x) and their elegant interrelations
- Euler product, M?bius inversion & the Mellin transform as you've never seen them
- Analytic continuation, the functional equation & the critical strip's beguiling zeros
- Perron's formula, contour shifting & explicit formulas connecting primes to zeros
- Zero-free regions (de la Vall?e Poussin, Vinogradov-Korobov) and their prime-counting payoffs
- Practical Python scripts for the Prime Number Theorem, error-term exploration, prime gaps & short-interval counts
- Conditional frontiers: Riemann Hypothesis, zero-density theorems, pair correlation & more

Why wade through abstract theorems alone when you can execute them? Each chapter marries rigorous mathematics with interactive code that:

  • Visualizes dx/log x integrals and li(x) corrections
  • Computes ψ(x) and π(x) to astronomical heights
  • Demonstrates explicit error bounds O(x e (-c√log x))
  • Explores L-functions, Dirichlet series & primes in arithmetic progressions

Elevate your understanding, astonish your peers, and finally justify why prime gaps sometimes feel like the punchlines of cosmic jokes. Ideal for advanced undergraduates, graduate students, research mathematicians and anyone hungry for the ultimate fusion of theory and code.

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