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, specific standpoint. The e-book offers 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 fundamental query thought of within the e-book is how the values of the Mellin remodel are disbursed (in a probabilistic sense), in situations the place the enter functionality is certainly algebro-geometric. this question is spoke back by way of the book's major theorem, utilizing a mix of geometric, specific, and group-theoretic equipment.
By delivering a brand new framework for learning Mellin transforms over finite fields, this booklet opens up a brand new manner for researchers to extra discover the subject.
Read or Download Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Annals of Mathematics Studies) PDF
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