Mastering Number Theory
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Home > Mathematics and Science Textbooks > Mathematics > Number theory > Mastering Number Theory: Analytic Number Theory I: Prime-Counting and the Riemann Zeta Function(Mastering Number Theory - Pure Mathematics from the Ground Up)
Mastering Number Theory: Analytic Number Theory I: Prime-Counting and the Riemann Zeta Function(Mastering Number Theory - Pure Mathematics from the Ground Up)

Mastering Number Theory: Analytic Number Theory I: Prime-Counting and the Riemann Zeta Function(Mastering Number Theory - Pure Mathematics from the Ground Up)


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About the Book

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, Möbius 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 Vallée 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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Product Details
  • ISBN-13: 9798282199734
  • Publisher: Independently Published
  • Publisher Imprint: Independently Published
  • Height: 229 mm
  • No of Pages: 306
  • Returnable: N
  • Spine Width: 16 mm
  • Weight: 462 gr
  • ISBN-10: 8282199737
  • Publisher Date: 02 May 2025
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: Mastering Number Theory - Pure Mathematics from the Ground Up
  • Sub Title: Analytic Number Theory I: Prime-Counting and the Riemann Zeta Function
  • Width: 152 mm


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Mastering Number Theory: Analytic Number Theory I: Prime-Counting and the Riemann Zeta Function(Mastering Number Theory - Pure Mathematics from the Ground Up)
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