Convolution And Equidistribution
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Convolution And Equidistribution
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 2012-01-24
Convolution And Equidistribution written by Nicholas M. Katz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-24 with Mathematics categories.
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.
Convolution And Equidistribution
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Author : Nicholas M. Katz
language : en
Publisher: Princeton University Press
Release Date : 2012-01-24
Convolution And Equidistribution written by Nicholas M. Katz and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-01-24 with Mathematics categories.
Convolution and Equidistribution explores an important aspect of number theory--the theory of exponential sums over finite fields and their Mellin transforms--from a new, categorical point of view. The book presents fundamentally important results and a plethora of examples, opening up new directions in the subject. The finite-field Mellin transform (of a function on the multiplicative group of a finite field) is defined by summing that function against variable multiplicative characters. The basic question considered in the book is how the values of the Mellin transform are distributed (in a probabilistic sense), in cases where the input function is suitably algebro-geometric. This question is answered by the book's main theorem, using a mixture of geometric, categorical, and group-theoretic methods. By providing a new framework for studying Mellin transforms over finite fields, this book opens up a new way for researchers to further explore the subject.
Convolution And Equidistribution
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Author : Nicholas M. Katz
language : en
Publisher:
Release Date : 1940
Convolution And Equidistribution written by Nicholas M. Katz and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1940 with Convolutions (Mathematics) categories.
The Second Moment Theory Of Families Of L Functions The Case Of Twisted Hecke L Functions
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Author : Valentin Blomer
language : en
Publisher: American Mathematical Society
Release Date : 2023-02-13
The Second Moment Theory Of Families Of L Functions The Case Of Twisted Hecke L Functions written by Valentin Blomer and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-02-13 with Mathematics categories.
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Probability Measures On Locally Compact Groups
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Author : H. Heyer
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability Measures On Locally Compact Groups written by H. Heyer and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Probability measures on algebraic-topological structures such as topological semi groups, groups, and vector spaces have become of increasing importance in recent years for probabilists interested in the structural aspects of the theory as well as for analysts aiming at applications within the scope of probability theory. In order to obtain a natural framework for a first systematic presentation of the most developed part of the work done in the field we restrict ourselves to prob ability measures on locally compact groups. At the same time we stress the non Abelian aspect. Thus the book is concerned with a set of problems which can be regarded either from the probabilistic or from the harmonic-analytic point of view. In fact, it seems to be the synthesis of these two viewpoints, the initial inspiration coming from probability and the refined techniques from harmonic analysis which made this newly established subject so fascinating. The goal of the presentation is to give a fairly complete treatment of the central limit problem for probability measures on a locally compact group. In analogy to the classical theory the discussion is centered around the infinitely divisible probability measures on the group and their relationship to the convergence of infinitesimal triangular systems.
Higher Order Fourier Analysis
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date : 2012-12-30
Higher Order Fourier Analysis written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-30 with Education categories.
Traditional Fourier analysis, which has been remarkably effective in many contexts, uses linear phase functions to study functions. Some questions, such as problems involving arithmetic progressions, naturally lead to the use of quadratic or higher order phases. Higher order Fourier analysis is a subject that has become very active only recently. Gowers, in groundbreaking work, developed many of the basic concepts of this theory in order to give a new, quantitative proof of Szemerédi's theorem on arithmetic progressions. However, there are also precursors to this theory in Weyl's classical theory of equidistribution, as well as in Furstenberg's structural theory of dynamical systems. This book, which is the first monograph in this area, aims to cover all of these topics in a unified manner, as well as to survey some of the most recent developments, such as the application of the theory to count linear patterns in primes. The book serves as an introduction to the field, giving the beginning graduate student in the subject a high-level overview of the field. The text focuses on the simplest illustrative examples of key results, serving as a companion to the existing literature on the subject. There are numerous exercises with which to test one's knowledge.
Relative Trace Formulas
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Author : Werner Müller
language : en
Publisher: Springer Nature
Release Date : 2021-05-18
Relative Trace Formulas written by Werner Müller and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-05-18 with Mathematics categories.
A series of three symposia took place on the topic of trace formulas, each with an accompanying proceedings volume. The present volume is the third and final in this series and focuses on relative trace formulas in relation to special values of L-functions, integral representations, arithmetic cycles, theta correspondence and branching laws. The first volume focused on Arthur’s trace formula, and the second volume focused on methods from algebraic geometry and representation theory. The three proceedings volumes have provided a snapshot of some of the current research, in the hope of stimulating further research on these topics. The collegial format of the symposia allowed a homogeneous set of experts to isolate key difficulties going forward and to collectively assess the feasibility of diverse approaches.
Probability Measures On Groups
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Author : H. Heyer
language : en
Publisher: Springer
Release Date : 2006-11-15
Probability Measures On Groups written by H. Heyer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
The Decomposition Of Global Conformal Invariants
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Author : Spyros Alexakis
language : en
Publisher:
Release Date : 1940
The Decomposition Of Global Conformal Invariants written by Spyros Alexakis and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1940 with Conformal invariants categories.
Handbook Of Finite Fields
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Author : Gary L. Mullen
language : en
Publisher: CRC Press
Release Date : 2013-06-17
Handbook Of Finite Fields written by Gary L. Mullen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-17 with Computers categories.
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and