Prime Numbers and the Riemann Hypothesis

ISBN-13: 9781107101920 / Angielski / Twarda / 2016 / 156 str.

Barry Mazur; William Stein

Opis

This book introduces prime numbers and explains the famous unsolved Riemann hypothesis.

Recenzje

'I really recommend this book if you want to get a feeling for the Riemann hypothesis without sinking into technicalities.' John Baez, The n-Category Café (http://golem.ph.utexas.edu/category)

Spis treści

1. Thoughts about numbers; 2. What are prime numbers?; 3. 'Named' prime numbers; 4. Sieves; 5. Questions about primes; 6. Further questions about primes; 7. How many primes are there?; 8. Prime numbers viewed from a distance; 9. Pure and applied mathematics; 10. A probabilistic 'first' guess; 11. What is a 'good approximation'?; 12. Square root error and random walks; 13. What is Riemann's hypothesis?; 14. The mystery moves to the error term; 15. Césaro smoothing; 16. A view of Li(X) - π(X); 17. The prime number theorem; 18. The staircase of primes; 19. Tinkering with the staircase of primes; 20. Computer music files and prime numbers; 21. The word 'spectrum'; 22. Spectra and trigonometric sums; 23. The spectrum and the staircase of primes; 24. To our readers of part I; 25. Slopes and graphs that have no slopes; 26. Distributions; 27. Fourier transforms: second visit; 28. Fourier transform of delta; 29. Trigonometric series; 30. A sneak preview; 31. On losing no information; 32. Going from the primes to the Riemann spectrum; 33. How many θi's are there?; 34. Further questions about the Riemann spectrum; 35. Going from the Riemann spectrum to the primes; 36. Building π(X) knowing the spectrum; 37. As Riemann envisioned it; 38. Companions to the zeta function.