{"product_id":"convolution-and-equidistribution-sato-tate-theorems-for-finite-field-mellin-transforms-9780691153315","title":"Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms","description":"\u003cp\u003e • Author(s): Nicholas M. Katz\u003cbr\u003e • Publisher: Princeton University Press\u003cbr\u003e • Publisher Imprint: Princeton University Press\u003cbr\u003e • BISAC: Calculus\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.","brand":"Princeton University Press","offers":[{"title":"Paperback","offer_id":46296553128087,"sku":"9780691153315","price":6728.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780691153315.webp?v=1769304993","url":"https:\/\/atlanticbooks.com\/products\/convolution-and-equidistribution-sato-tate-theorems-for-finite-field-mellin-transforms-9780691153315","provider":"Atlantic Books","version":"1.0","type":"link"}