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 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.

Show description

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

Best Algebraic Geometry books

Analytic K-Homology (Oxford Mathematical Monographs)

This paintings attracts jointly rules from algebraic topology, useful research and geometry. it's a device - a method of conveying info between those 3 matters - and it's been used with luck to find theorems throughout a large span of arithmetic. the aim of this e-book is to acquaint the reader with the fundamental principles of analytic K-homology and enhance a few of its functions.

The Geometry of Topological Stability (London Mathematical Society Monographs)

In featuring an in depth learn of the geometry and topology of diverse sessions of "generic" singularities, Geometry of Topological balance bridges the space among algebraic calculations and continuity arguments to aspect the required and enough stipulations for a C (infinity) to be C]0-stable. all through, the authors masterfully learn this crucial topic utilizing effects culled from a huge diversity of mathematical disciplines, together with geometric topology, stratification concept, algebraic geometry, and commutative algebra.

Lectures on Polytopes (Graduate Texts in Mathematics)

In response to a graduate direction on the Technische Universit├Ąt, Berlin, those lectures current a wealth of fabric at the sleek conception of convex polytopes. the simple exposition positive factors many illustrations, and whole proofs for many theorems. With merely linear algebra as a prerequisite, it takes the reader quick from the fundamentals to subject matters of contemporary examine.

Higher-Dimensional Algebraic Geometry (Universitext)

The category thought of algebraic forms is the point of interest of this e-book. This very lively zone of study continues to be constructing, yet an grand volume of data has collected over the last 20 years. The authors target is to supply an simply available advent to the topic. The booklet begins with preparatory and traditional definitions and effects, then strikes directly to speak about a variety of facets of the geometry of delicate projective types with many rational curves, and finishes in taking the 1st steps in the direction of Moris minimum version application of class of algebraic kinds by means of proving the cone and contraction theorems.

Additional resources for Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (AM-180) (Annals of Mathematics Studies)

Show sample text content

Rated 4.75 of 5 – based on 18 votes