By Nicholas M. Katz
Convolution and Equidistribution explores an enormous point of quantity theory--the thought of exponential sums over finite fields and their Mellin transforms--from a brand new, specific standpoint. The publication offers essentially very important effects and a plethora of examples, commencing up new instructions within the topic.
The finite-field Mellin remodel (of a functionality at the multiplicative staff of a finite box) is outlined via summing that functionality opposed to variable multiplicative characters. the fundamental query thought of within the booklet is how the values of the Mellin rework are allotted (in a probabilistic sense), in situations the place the enter functionality is certainly algebro-geometric. this query is responded 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 means for researchers to extra discover the subject.
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