Riemann's zeta function
by Harold M. Edwards · first published 1974
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…Mathematics (John Derbyshire, 2004) 4. Unknown Quantity: A Real and Imaginary History of Algebra (John Derbyshire, 2007) 5. Journey through Genius: The Great Theorems of Mathematics (William Dunham, 1991) 6. Riemann’s Zeta Function (H. M. Edwards, 1971) 7. Gamma: Exploring Euler’s Constant (Julian Havil, 2009) 8. The Man Who Loved Only Numbers (Paul Hoffman, 1999) 9. The Riemann Zeta-Function: Theory and Applications. (Alexander…
on “The Riemann Hypothesis, explained” ↗If you've got enough math background to follow it, Harold Edwards' Riemann's Zeta Function is a gem of a book and available inexpensively from Dover. There is an English translation of Riemann's paper at the end of the book. I spent a worthwhile few weeks of spare time working my way through…
on “The Riemann Hypothesis” ↗Hm, except for using Gamma(n) = (n-1)! instead of Pi(n) = n!, this presentation seems to follow the notation of this book: https://books.google.ca/books/about/Riemann_s_Zeta_Function.... This is most obvious in the naming of the J function near the bottom, which I have not seen anywhere else. Riemann originally called that function a generic f. At any rate, Edwards' book is great…
on “The Riemann Hypothesis, explained” ↗…Zipf distribution takes this shape when the vocabulary is infinite: P(r)=r^-s / Zeta(s) with s > 1 Replace r^-s with (r + a)^-s, i.e. move onto Mandelbrot's rank-shifted model of Zipf's law and Riemann's Zeta function becomes Hurwitz Zeta function (ZetaHurwitz(s,a+1) with the ranks starting at 1). Zipf law != Zipf distribution, still this is intriguing. Integers and Prime Numbers: Deriving Zipf's Law (https://arxiv.org/abs/2403.12773)…
on “What does the Riemann zeta function have to do with the distribution of primes?” ↗