{"product_id":"9783540783787","title":"Arithmetical Investigations","description":"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.","brand":"Shai M. J. Haran","offers":[{"title":"Default Title","offer_id":47589906612542,"sku":"9783540783787","price":1970.99,"currency_code":"ZAR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9783540783787.jpg?v=1707722415","url":"https:\/\/exclusivebooks.co.za\/products\/9783540783787","provider":"Exclusive Books Online","version":"1.0","type":"link"}