Convolution and Equidistribution: Sato-Tate Theorems for by Nicholas M. Katz

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, express viewpoint. The booklet provides essentially very important effects and a plethora of examples, commencing up new instructions within the subject.

The finite-field Mellin rework (of a functionality at the multiplicative team of a finite box) is outlined via summing that functionality opposed to variable multiplicative characters. the fundamental query thought of within the e-book is how the values of the Mellin rework are allotted (in a probabilistic sense), in instances the place the enter functionality is definitely algebro-geometric. this query is replied through the book's major theorem, utilizing a mix of geometric, express, and group-theoretic methods.

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.

Show description

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

Similar group theory books

Operator Algebras: Theory of C*-Algebras and von Neumann Algebras: 122 (Encyclopaedia of Mathematical Sciences)

This booklet deals a entire creation to the overall conception of C*-algebras and von Neumann algebras. starting with the fundamentals, the speculation is built via such subject matters as tensor items, nuclearity and exactness, crossed items, K-theory, and quasidiagonality. The presentation conscientiously and accurately explains the most good points of every a part of the speculation of operator algebras; most vital arguments are at the least defined and plenty of are provided in complete aspect.

Symmetries and Groups in Contemporary Physics (Nankai Series in Pure, Applied Mathematics and Theoretical Physics)

This quantity makes a speciality of advancements within the box of staff conception in its broadest experience and is of curiosity to theoretical and experimental physicists, mathematicians, and scientists in comparable disciplines who're drawn to the newest tools and functions. In an more and more ultra-specialized global, this quantity will show the interchange of rules and techniques in theoretical and mathematical physics.

Basic Algebraic Topology and its Applications

This ebook presents an obtainable advent to algebraic topology, a field on the intersection of topology, geometry and algebra, including its purposes. in addition, it covers numerous similar issues which are in reality vital within the total scheme of algebraic topology. Comprising eighteen chapters and appendices, the e-book integrates a number of suggestions of algebraic topology, supported by way of examples, workouts, purposes and ancient notes.

Finite and Profinite Quantum Systems (Quantum Science and Technology)

This monograph offers an creation to finite quantum platforms, a box on the interface among quantum details and quantity conception, with functions in quantum computation and condensed topic physics. the 1st significant a part of this monograph reviews the so-called `qubits' and `qudits', structures with periodic finite lattice as place area.

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

Example text

Download PDF sample

Rated 4.24 of 5 – based on 9 votes