Arithmetical Investigations
Download Arithmetical Investigations full books in PDF, epub, and Kindle. Read online free Arithmetical Investigations ebook anywhere anytime directly on your device. Fast Download speed and no annoying ads. We cannot guarantee that every ebooks is available!
Arithmetical Investigations
Author | : Shai M. J. Haran |
Publisher | : Springer Science & Business Media |
Total Pages | : 224 |
Release | : 2008-04-25 |
Genre | : Mathematics |
ISBN | : 3540783784 |
Download Arithmetical Investigations Book in PDF, Epub and Kindle
In this volume the author further develops his philosophy of quantum interpolation between the real numbers and the p-adic numbers. The p-adic numbers contain the p-adic integers Zp which are the inverse limit of the finite rings Z/pn. This gives rise to a tree, and probability measures w on Zp correspond to Markov chains on this tree. From the tree structure one obtains special basis for the Hilbert space L2(Zp,w). The real analogue of the p-adic integers is the interval [-1,1], and a probability measure w on it gives rise to a special basis for L2([-1,1],w) - the orthogonal polynomials, and to a Markov chain on "finite approximations" of [-1,1]. For special (gamma and beta) measures there is a "quantum" or "q-analogue" Markov chain, and a special basis, that within certain limits yield the real and the p-adic theories. This idea can be generalized variously. In representation theory, it is the quantum general linear group GLn(q)that interpolates between the p-adic group GLn(Zp), and between its real (and complex) analogue -the orthogonal On (and unitary Un )groups. There is a similar quantum interpolation between the real and p-adic Fourier transform and between the real and p-adic (local unramified part of) Tate thesis, and Weil explicit sums.
Arithmetical Investigations Related Books
Pages: 224
Pages: 32
Pages: 491
Pages: 232
Pages: 0