…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…
…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…
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…
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…
…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)…
…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…
…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…
如果你有足够的数学底子能看懂的话，Harold Edwards 的《Riemann's Zeta Function》绝对是神作一本，而且 Dover 出版社出的版本很便宜。书末还附有黎曼那篇论文的英译本。我花了好几个礼拜的业余时间把它啃了下来，收获颇丰……
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…
嗯，除了用 Gamma(n) = (n-1)! 代替 Pi(n) = n! 之外，这个介绍的符号体系似乎遵循了这本书：https://books.google.ca/books/about/Riemann_s_Zeta_Function.... 最明显的地方就是底部附近的 J 函数命名，这在其他任何地方我都还没见过。黎曼最初把那个函数泛称为 f。不管怎样，Edwards 那本书写得很棒……
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…
……当词表无限大时，齐普夫分布（Zipf distribution）就呈现出这种形式：P(r)=r^-s / Zeta(s)，其中 s > 1。将 r^-s 替换为 (r + a)^-s，也就是采用曼德博（Mandelbrot）的秩位移齐普夫定律模型，黎曼 Zeta 函数就变成了赫尔维茨（Hurwitz）Zeta 函数（从排名 1 开始记为 ZetaHurwitz(s,a+1)）。齐普夫定律 != 齐普夫分布，但这依然非常耐人寻味。《整数与素数：推导齐普夫定律》（https://arxiv.org/abs/2403.12773）……
…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)…