Download E-books Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Annals of Mathematics Studies) PDF

By Nicholas M. Katz

Convolution and Equidistribution explores an incredible element of quantity theory--the thought of exponential sums over finite fields and their Mellin transforms--from a brand new, express perspective. The e-book provides essentially very important effects and a plethora of examples, establishing up new instructions within the topic.

The finite-field Mellin remodel (of a functionality at the multiplicative team of a finite box) is outlined by way of summing that functionality opposed to variable multiplicative characters. the elemental query thought of within the ebook is how the values of the Mellin rework are disbursed (in a probabilistic sense), in instances the place the enter functionality is certainly algebro-geometric. this question is responded through the book's major theorem, utilizing a mix of geometric, specific, and group-theoretic equipment.

By offering a brand new framework for learning Mellin transforms over finite fields, this publication opens up a brand new approach for researchers to additional discover the subject.

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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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