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Convolution And Equidistribution
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Book Synopsis Convolution and Equidistribution by : Nicholas M. Katz
Download or read book Convolution and Equidistribution written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2012-01-24 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Convolution and Equidistribution by : Nicholas M. Katz
Download or read book Convolution and Equidistribution written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2012-01-24 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Probability Measures on Locally Compact Groups by : H. Heyer
Download or read book Probability Measures on Locally Compact Groups written by H. Heyer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Second Moment Theory of Families of $L$-Functions–The Case of Twisted Hecke $L$-Functions by : Valentin Blomer
Download or read book The Second Moment Theory of Families of $L$-Functions–The Case of Twisted Hecke $L$-Functions written by Valentin Blomer and published by American Mathematical Society. This book was released on 2023-02-13 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: View the abstract.
Book Synopsis Probability Measures on Groups by : H. Heyer
Download or read book Probability Measures on Groups written by H. Heyer and published by Springer. This book was released on 2006-11-15 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (Am-180) by : Nicholas M. Katz
Download or read book Convolution and Equidistribution: Sato-Tate Theorems for Finite-Field Mellin Transforms (Am-180) written by Nicholas M. Katz and published by . This book was released on 2012-01-01 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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.
Book Synopsis Relative Trace Formulas by : Werner Müller
Download or read book Relative Trace Formulas written by Werner Müller and published by Springer Nature. This book was released on 2021-05-18 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Equidistribution in Number Theory, An Introduction by : Andrew Granville
Download or read book Equidistribution in Number Theory, An Introduction written by Andrew Granville and published by Springer Science & Business Media. This book was released on 2007-04-08 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This set of lectures provides a structured introduction to the concept of equidistribution in number theory. This concept is of growing importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos. The volume brings together leading researchers from a range of fields who reveal fascinating links between seemingly disparate areas.
Book Synopsis The Dynkin Festschrift by : Mark I. Freidlin
Download or read book The Dynkin Festschrift written by Mark I. Freidlin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116 by : Nicholas M. Katz
Download or read book Gauss Sums, Kloosterman Sums, and Monodromy Groups. (AM-116), Volume 116 written by Nicholas M. Katz and published by Princeton University Press. This book was released on 2016-03-02 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.
Book Synopsis Integration and Cubature Methods by : Willi Freeden
Download or read book Integration and Cubature Methods written by Willi Freeden and published by CRC Press. This book was released on 2017-11-22 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: In industry and economics, the most common solutions of partial differential equations involving multivariate numerical integration over cuboids include techniques of iterated one-dimensional approximate integration. In geosciences, however, the integrals are extended over potato-like volumes (such as the ball, ellipsoid, geoid, or the Earth) and their boundary surfaces which require specific multi-variate approximate integration methods. Integration and Cubature Methods: A Geomathematically Oriented Course provides a basic foundation for students, researchers, and practitioners interested in precisely these areas, as well as breaking new ground in integration and cubature in geomathematics.
Book Synopsis Decorrelative Mollifier Gravimetry by : Willi Freeden
Download or read book Decorrelative Mollifier Gravimetry written by Willi Freeden and published by Springer Nature. This book was released on 2021-05-12 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the geoscientific context arising in decorrelative gravitational exploration to determine the mass density distribution inside the Earth. First, an insight into the current state of research is given by reducing gravimetry to mathematically accessible, and thus calculable, decorrelated models. In this way, the various unresolved questions and problems of gravimetry are made available to a broad scientific audience and the exploration industry. New theoretical developments will be given, and innovative ways of modeling geologic layers and faults by mollifier regularization techniques are shown. This book is dedicated to surface as well as volume geology with potential data primarily of terrestrial origin. For deep geology, the geomathematical decorrelation methods are to be designed in such a way that depth information (e.g., in boreholes) may be canonically entered. Bridging several different geo-disciplines, this book leads in a cycle from the potential measurements made by geoengineers, to the cleansing of data by geophysicists and geoengineers, to the subsequent theory and model formation, computer-based implementation, and numerical calculation and simulations made by geomathematicians, to interpretation by geologists, and, if necessary, back. It therefore spans the spectrum from geoengineering, especially geodesy, via geophysics to geomathematics and geology, and back. Using the German Saarland area for methodological tests, important new fields of application are opened, particularly for regions with mining-related cavities or dense development in today's geo-exploration.
Book Synopsis Analytic Methods in Applied Probability by : Yu. M. Suhov
Download or read book Analytic Methods in Applied Probability written by Yu. M. Suhov and published by American Mathematical Soc.. This book was released on 2002 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is dedicated to F. I. Karpelevich, an outstanding Russian mathematician who made important contributions to applied probability theory. The book contains original papers focusing on several areas of applied probability and its uses in modern industrial processes, telecommunications, computing, mathematical economics, and finance. It opens with a review of Karpelevich's contributions to applied probability theory and includes a bibliography of his works. Other articles discuss queueing network theory, in particular, in heavy traffic approximation (fluid models). The book is suitable for graduate students, theoretical and applied probabilists, computer scientists, and engineers.
Book Synopsis Gauss Sums, Kloosterman Sums, and Monodromy Groups by : Nicholas M. Katz
Download or read book Gauss Sums, Kloosterman Sums, and Monodromy Groups written by Nicholas M. Katz and published by Princeton University Press. This book was released on 1988 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: The study of exponential sums over finite fields, begun by Gauss nearly two centuries ago, has been completely transformed in recent years by advances in algebraic geometry, culminating in Deligne's work on the Weil Conjectures. It now appears as a very attractive mixture of algebraic geometry, representation theory, and the sheaf-theoretic incarnations of such standard constructions of classical analysis as convolution and Fourier transform. The book is simultaneously an account of some of these ideas, techniques, and results, and an account of their application to concrete equidistribution questions concerning Kloosterman sums and Gauss sums.
Download or read book Séminaire Bourbaki written by and published by . This book was released on 2019 with total page 644 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Groups St Andrews 2013 by : C. M. Campbell
Download or read book Groups St Andrews 2013 written by C. M. Campbell and published by Cambridge University Press. This book was released on 2015-10-22 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: Every four years, leading researchers gather to survey the latest developments in all aspects of group theory. Since 1981, the proceedings of those meetings have provided a regular snapshot of the state of the art in group theory and helped to shape the direction of research in the field. This volume contains selected papers from the 2013 meeting held in St Andrews. It begins with major articles from each of the four main speakers: Emmanuel Breuillard (Paris-Sud), Martin Liebeck (Imperial College London), Alan Reid (Texas) and Karen Vogtmann (Cornell). These are followed by, in alphabetical order, survey articles contributed by other conference participants, which cover a wide spectrum of modern group theory.
Download or read book Fourier Analysis written by T. W. Körner and published by Cambridge University Press. This book was released on 2022-06-09 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Fourier analysis is a subject that was born in physics but grew up in mathematics. Now it is part of the standard repertoire for mathematicians, physicists and engineers. This diversity of interest is often overlooked, but in this much-loved book, Tom Körner provides a shop window for some of the ideas, techniques and elegant results of Fourier analysis, and for their applications. These range from number theory, numerical analysis, control theory and statistics, to earth science, astronomy and electrical engineering. The prerequisites are few (a reader with knowledge of second- or third-year undergraduate mathematics should have no difficulty following the text), and the style is lively and entertaining. This edition of Körner's 1989 text includes a foreword written by Professor Terence Tao introducing it to a new generation of fans.
