By Nicholas M. Katz
Convolution and Equidistribution explores a major point of quantity theory--the concept of exponential sums over finite fields and their Mellin transforms--from a brand new, express viewpoint. The booklet provides essentially very important effects and a plethora of examples, commencing up new instructions within the subject.
The finite-field Mellin rework (of a functionality at the multiplicative team of a finite box) is outlined via summing that functionality opposed to variable multiplicative characters. the fundamental query thought of within the e-book is how the values of the Mellin rework are allotted (in a probabilistic sense), in instances the place the enter functionality is definitely algebro-geometric. this query is replied through the book's major theorem, utilizing a mix of geometric, express, and group-theoretic methods.
By supplying a brand new framework for learning Mellin transforms over finite fields, this publication opens up a brand new means for researchers to extra discover the subject.
Read Online or Download Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Annals of Mathematics Studies) PDF
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Extra resources for Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Annals of Mathematics Studies)