{"product_id":"mastering-number-theory-analytic-number-theory-i-prime-8208-counting-and-the-riemann-zeta-function-9798282199734","title":"Mastering Number Theory: Analytic Number Theory I: Prime\u0026#8208;Counting and the Riemann Zeta Function","description":"\u003cp\u003e • Author(s): Alexei Nowakowski\u003cbr\u003e • Publisher: Independently Published\u003cbr\u003e • Publisher Imprint: Independently Published\u003cbr\u003e • BISAC: Number Theory\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eWarning: counting primes may induce an irrational obsession-fortunately, unlike π, your sanity here is well within finite bounds.\u003c\/p\u003e \u003cp\u003ePrepare 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 \u003cb\u003efull Python demos\u003c\/b\u003e-guides you through: \u003c\/p\u003e \u003cp\u003e- Foundations of π(x), θ(x), ψ(x) and their elegant interrelations\u003cbr\u003e- Euler product, M?bius inversion \u0026amp; the Mellin transform as you've never seen them\u003cbr\u003e- Analytic continuation, the functional equation \u0026amp; the critical strip's beguiling zeros\u003cbr\u003e- Perron's formula, contour shifting \u0026amp; explicit formulas connecting primes to zeros\u003cbr\u003e- Zero-free regions (de la Vall?e Poussin, Vinogradov-Korobov) and their prime-counting payoffs\u003cbr\u003e- Practical Python scripts for the Prime Number Theorem, error-term exploration, prime gaps \u0026amp; short-interval counts\u003cbr\u003e- Conditional frontiers: Riemann Hypothesis, zero-density theorems, pair correlation \u0026amp; more\u003c\/p\u003e \u003cp\u003eWhy wade through abstract theorems alone when you can \u003cb\u003eexecute\u003c\/b\u003e them? Each chapter marries rigorous mathematics with interactive code that: \u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eVisualizes dx\/log x integrals and li(x) corrections\u003c\/li\u003e\n\u003cli\u003eComputes ψ(x) and π(x) to astronomical heights\u003c\/li\u003e\n\u003cli\u003eDemonstrates explicit error bounds O(x e (-c√log x))\u003c\/li\u003e\n\u003cli\u003eExplores L-functions, Dirichlet series \u0026amp; primes in arithmetic progressions\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003eElevate 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.\u003cbr\u003e","brand":"Independently Published","offers":[{"title":"Paperback","offer_id":45559739613335,"sku":"9798282199734","price":2413.0,"currency_code":"INR","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9798282199734.webp?v=1767678026","url":"https:\/\/atlanticbooks.com\/products\/mastering-number-theory-analytic-number-theory-i-prime-8208-counting-and-the-riemann-zeta-function-9798282199734","provider":"Atlantic Books","version":"1.0","type":"link"}