{"product_id":"convolution-and-equidistribution-sato-tate-theorems-for-finite-field-mellin-transforms-paperback","title":"Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms - Paperback","description":"\u003cdiv\u003e\u003cp style=\"text-align: right;\"\u003e\u003ca href=\"https:\/\/reportcopyrightinfringement.com\/\" target=\"_blank\" rel=\"nofollow\"\u003e\u003cb\u003eReport copyright infringement\u003c\/b\u003e\u003c\/a\u003e\u003c\/p\u003e\u003c\/div\u003e\u003cp\u003eby \u003cb\u003eNicholas M. Katz\u003c\/b\u003e (Author)\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eConvolution and Equidistribution\u003c\/i\u003e explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. \u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. \u003cp\u003e\u003c\/p\u003e By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.\u003ch3\u003eAuthor Biography\u003c\/h3\u003e\u003cp\u003e\u003cb\u003eNicholas M. Katz\u003c\/b\u003e is professor of mathematics at Princeton University. He is the author or coauthor of six previous titles in the Annals of Mathematics Studies: \u003ci\u003eArithmetic Moduli of Elliptic Curves \u003c\/i\u003e(with Barry Mazur); \u003ci\u003eGauss Sums, Kloosterman Sums, and Monodromy Groups\u003c\/i\u003e; \u003ci\u003eExponential Sums and Differential Equations\u003c\/i\u003e; \u003ci\u003eRigid Local Systems\u003c\/i\u003e; \u003ci\u003eTwisted L-Functions and Monodromy;\u003c\/i\u003e and \u003ci\u003eMoments, Monodromy, and Perversity.\u003c\/i\u003e\u003c\/p\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eNumber of Pages:\u003c\/strong\u003e 208\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003eDimensions:\u003c\/strong\u003e 0.6 x 9.1 x 6.1 IN\u003c\/div\u003e\n            \u003cdiv\u003e\n\u003cstrong\u003ePublication Date:\u003c\/strong\u003e January 24, 2012\u003c\/div\u003e\n            ","brand":"BooksCloud","offers":[{"title":"Default Title","offer_id":47748929552633,"sku":"9780691153315","price":188.1,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0789\/2782\/3097\/files\/Fp-2qsSgRR9780691153315.webp?v=1775548099","url":"https:\/\/bookscloud.io\/products\/convolution-and-equidistribution-sato-tate-theorems-for-finite-field-mellin-transforms-paperback","provider":"BooksCloud Book Dropshipping","version":"1.0","type":"link"}