Convolution and Equidistribution PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Convolution and Equidistribution PDF full book. Access full book title Convolution and Equidistribution by Nicholas M. Katz. Download full books in PDF and EPUB format.
Author: Nicholas M. Katz
Publisher: Princeton University Press
ISBN: 1400842700
Category : Mathematics
Languages : en
Pages : 213
Get Book Here
Book Description
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.
Author: Nicholas M. Katz
Publisher: Princeton University Press
ISBN: 1400842700
Category : Mathematics
Languages : en
Pages : 213
Get Book Here
Book Description
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.
Author: Nicholas M. Katz
Publisher:
ISBN: 9781283379960
Category : Mathematics
Languages : en
Pages : 203
Get Book Here
Book Description
"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.
Author: Nicholas M. Katz
Publisher:
ISBN:
Category : Convolutions (Mathematics)
Languages : en
Pages : 216
Get Book Here
Book Description
Author: H. Heyer
Publisher: Springer Science & Business Media
ISBN: 3642667066
Category : Mathematics
Languages : en
Pages : 542
Get Book Here
Book Description
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.
Author: H. Heyer
Publisher: Springer
ISBN: 3540354069
Category : Mathematics
Languages : en
Pages : 366
Get Book Here
Book Description
Author: Valentin Blomer
Publisher: American Mathematical Society
ISBN: 1470456788
Category : Mathematics
Languages : en
Pages : 160
Get Book Here
Book Description
View the abstract.
Author: David Vernon Widder
Publisher:
ISBN: 9780691626925
Category : Science
Languages : en
Pages : 0
Get Book Here
Book Description
Annotation The description for this book, Convolution Transform, will be forthcoming.
Author: Wilhelm Kecs
Publisher:
ISBN:
Category : Convolutions (Mathematics)
Languages : en
Pages : 321
Get Book Here
Book Description
Author: Werner Müller
Publisher: Springer Nature
ISBN: 3030685063
Category : Mathematics
Languages : en
Pages : 438
Get Book Here
Book Description
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.
Author: Mark I. Freidlin
Publisher: Springer Science & Business Media
ISBN: 1461202795
Category : Mathematics
Languages : en
Pages : 433
Get Book Here
Book Description
Onishchik, A. A. Kirillov, and E. B. Vinberg, who obtained their first results on Lie groups in Dynkin's seminar. At a later stage, the work of the seminar was greatly enriched by the active participation of 1. 1. Pyatetskii Shapiro. As already noted, Dynkin started to work in probability as far back as his undergraduate studies. In fact, his first published paper deals with a problem arising in Markov chain theory. The most significant among his earliest probabilistic results concern sufficient statistics. In [15] and [17], Dynkin described all families of one-dimensional probability distributions admitting non-trivial sufficient statistics. These papers have considerably influenced the subsequent research in this field. But Dynkin's most famous results in probability concern the theory of Markov processes. Following Kolmogorov, Feller, Doob and Ito, Dynkin opened a new chapter in the theory of Markov processes. He created the fundamental concept of a Markov process as a family of measures corresponding to var ious initial times and states and he defined time homogeneous processes in terms of the shift operators ()t. In a joint paper with his student A.
