By Nicholas M. Katz
Convolution and Equidistribution explores a big point of quantity theory--the concept of exponential sums over finite fields and their Mellin transforms--from a brand new, specific perspective. The ebook offers essentially vital effects and a plethora of examples, commencing up new instructions within the topic.
The finite-field Mellin remodel (of a functionality at the multiplicative crew of a finite box) is outlined via summing that functionality opposed to variable multiplicative characters. the elemental query thought of within the ebook is how the values of the Mellin remodel are allotted (in a probabilistic sense), in situations the place the enter functionality is certainly algebro-geometric. this question is replied through the book's major theorem, utilizing a mix of geometric, specific, and group-theoretic tools.
By supplying a brand new framework for learning Mellin transforms over finite fields, this publication opens up a brand new approach 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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