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An Introduction To Non Abelian Class Field Theory
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Book Synopsis An Introduction to Non-Abelian Class Field Theory by : Toyokazu Hiramatsu
Download or read book An Introduction to Non-Abelian Class Field Theory written by Toyokazu Hiramatsu and published by World Scientific. This book was released on 2016-09-13 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.
Author :Toyokazu Hiramatsu Publisher :World Scientific Publishing Company ISBN 13 :9789813142268 Total Pages :175 pages Book Rating :4.1/5 (422 download)
Book Synopsis An Introduction to Non-Abelian Class Field Theory by : Toyokazu Hiramatsu
Download or read book An Introduction to Non-Abelian Class Field Theory written by Toyokazu Hiramatsu and published by World Scientific Publishing Company. This book was released on 2017 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1.
Book Synopsis An Introduction to Non-Abelian Class Field Theory by : Toyokazu Hiramatsu
Download or read book An Introduction to Non-Abelian Class Field Theory written by Toyokazu Hiramatsu and published by . This book was released on 2016 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This monograph provides a brief exposition of automorphic forms of weight 1 and their applications to arithmetic, especially to Galois representations. One of the outstanding problems in arithmetic is a generalization of class field theory to non-abelian Galois extension of number fields. In this volume, we discuss some relations between this problem and cusp forms of weight 1."--Publisher's website.
Book Synopsis Class Field Theory by : Nancy Childress
Download or read book Class Field Theory written by Nancy Childress and published by Springer Science & Business Media. This book was released on 2008-10-28 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: Class field theory brings together the quadratic and higher reciprocity laws of Gauss, Legendre, and others, and vastly generalizes them. This book provides an accessible introduction to class field theory. It takes a traditional approach in that it attempts to present the material using the original techniques of proof, but in a fashion which is cleaner and more streamlined than most other books on this topic. It could be used for a graduate course on algebraic number theory, as well as for students who are interested in self-study. The book has been class-tested, and the author has included lots of challenging exercises throughout the text.
Book Synopsis Class Field Theory by : Georges Gras
Download or read book Class Field Theory written by Georges Gras and published by Springer Science & Business Media. This book was released on 2005-02-16 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: Global class field theory is a major achievement of algebraic number theory based on the functorial properties of the reciprocity map and the existence theorem. This book explores the consequences and the practical use of these results in detailed studies and illustrations of classical subjects. In the corrected second printing 2005, the author improves many details all through the book.
Book Synopsis Knots and Primes by : Masanori Morishita
Download or read book Knots and Primes written by Masanori Morishita and published by Springer Nature. This book was released on with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Class Field Theory written by J. Neukirch and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Class field theory, which is so immediately compelling in its main assertions, has, ever since its invention, suffered from the fact that its proofs have required a complicated and, by comparison with the results, rather imper spicuous system of arguments which have tended to jump around all over the place. My earlier presentation of the theory [41] has strengthened me in the belief that a highly elaborate mechanism, such as, for example, cohomol ogy, might not be adequate for a number-theoretical law admitting a very direct formulation, and that the truth of such a law must be susceptible to a far more immediate insight. I was determined to write the present, new account of class field theory by the discovery that, in fact, both the local and the global reciprocity laws may be subsumed under a purely group theoretical principle, admitting an entirely elementary description. This de scription makes possible a new foundation for the entire theory. The rapid advance to the main theorems of class field theory which results from this approach has made it possible to include in this volume the most important consequences and elaborations, and further related theories, with the excep tion of the cohomology version which I have this time excluded. This remains a significant variant, rich in application, but its principal results should be directly obtained from the material treated here.
Book Synopsis Knots and Primes by : Masanori Morishita
Download or read book Knots and Primes written by Masanori Morishita and published by Springer Science & Business Media. This book was released on 2011-11-27 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a foundation for arithmetic topology - a new branch of mathematics which is focused upon the analogy between knot theory and number theory. Starting with an informative introduction to its origins, namely Gauss, this text provides a background on knots, three manifolds and number fields. Common aspects of both knot theory and number theory, for instance knots in three manifolds versus primes in a number field, are compared throughout the book. These comparisons begin at an elementary level, slowly building up to advanced theories in later chapters. Definitions are carefully formulated and proofs are largely self-contained. When necessary, background information is provided and theory is accompanied with a number of useful examples and illustrations, making this a useful text for both undergraduates and graduates in the field of knot theory, number theory and geometry.
Book Synopsis Class Field Theory: Proofs and Applications by : Daniel Fretwell
Download or read book Class Field Theory: Proofs and Applications written by Daniel Fretwell and published by GRIN Verlag. This book was released on 2011-07-27 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt: Research Paper from the year 2011 in the subject Mathematics - Number Theory, grade: Postgraduate, University of Sheffield, language: English, abstract: This document is a continuation of my Semester 1 project on class field theory. In the previous work, we made a rounded exposition of the fundamentals of class field theory but in order to preserve the document length the main proofs had to be skipped. We concentrate on filling in the gaps in this second installment. Due to the need to complete the arguments left open last semester and the need for applications this part of the project is a little longer than it should have been. It was not mentioned in the previous project but the class field theory we are studying here is global class field theory. There is such a thing as local class field theory in which we study the Abelian extensions of local fields (essentially fields that arise as completions of a number field with respect to places). Actually we touch on these ideas slightly in this project but never quite get to de_ning a local Artin map and looking at the local analogues of the main theorems of global class field theory. For those wanting to continue on to study local class field theory, consider Chapter 7 of [2] To start off this project we shall first restate the main de_nitions and theorems. This will be brief and those wanting to remind themselves of the details should consult my Semester 1 project. There will be very little motivation or technical results here since this was the purpose of the work done previously. We then set out to prove the main theorems of class field theory. With our present knowledge this would not be a simple task and we soon find that we first have to invent or discover new concepts such as the idele group and the corresponding idele class group. These are topological devices that take stock of all completions of a number eld at once. Such constructions will make the theory much easier to understand and formulate, whilst at the same time generalising the theory to all Abelian extensions. The cohomology of nite Abelian groups will be introduced and used alongside the idele theory to establish an important inequality. We use L-series in conjunction with the ideal theory to establish another important inequality. Combining the two inequalities will give a nice result that allows us to prove Artin reciprocity. In order to prove the existence theorem we resort to using Kummer n-extensions and the notion of a class eld. This middle chunk of the project will be quite technical but hopefully enjoyable and illuminating. [...]
Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Book Synopsis From Vehicles To Grid To Electric Vehicles To Green Grid: Many A Little Makes A Miracle by : Li Fuhuo
Download or read book From Vehicles To Grid To Electric Vehicles To Green Grid: Many A Little Makes A Miracle written by Li Fuhuo and published by World Scientific. This book was released on 2019-07-24 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book paves the way for a proper understanding of current and future issues on global warming, air pollution, depletion of natural resources, cyberattacks on smart grids, amongst others, by unifying various diverse disciplines of science to focus on a sustainable green society of the future.Readers will find applications of science described through the practical use of mobilities, in this case, the electric vehicles.The book could be used to teach and study on issues of global warming through the window of electric vehicles. The first three chapters can be used for teaching applications of mechanics, quantum mechanics, thermodynamics, and fluid mechanics. Chapter 5 provides rudiments of control theory in anticipation of control theory through number theory and algebraic geometry. Chapters 6 and 7 contain aspects of climatology, global warming, and electric vehicles to green grid. This is the only such comprehensive introductory book in the market that provides the readers hints, suggestions and directions to ponder for a sustainable future through renewable sources.
Book Synopsis Elementary Modular Iwasawa Theory by : Haruzo Hida
Download or read book Elementary Modular Iwasawa Theory written by Haruzo Hida and published by World Scientific. This book was released on 2021-10-04 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the first to provide a comprehensive and elementary account of the new Iwasawa theory innovated via the deformation theory of modular forms and Galois representations. The deformation theory of modular forms is developed by generalizing the cohomological approach discovered in the author's 2019 AMS Leroy P Steele Prize-winning article without using much algebraic geometry.Starting with a description of Iwasawa's classical results on his proof of the main conjecture under the Kummer-Vandiver conjecture (which proves cyclicity of his Iwasawa module more than just proving his main conjecture), we describe a generalization of the method proving cyclicity to the adjoint Selmer group of every ordinary deformation of a two-dimensional Artin Galois representation.The fundamentals in the first five chapters are as follows:Many open problems are presented to stimulate young researchers pursuing their field of study.
Book Synopsis Hilbert, Göttingen and the Development of Modern Mathematics by : Joan Roselló
Download or read book Hilbert, Göttingen and the Development of Modern Mathematics written by Joan Roselló and published by Cambridge Scholars Publishing. This book was released on 2019-02-01 with total page 295 pages. Available in PDF, EPUB and Kindle. Book excerpt: David Hilbert is one of the outstanding mathematicians of the twentieth century and probably the most influential. This book highlights Hilbert’s contributions to mathematics, putting them in their historical, social and cultural context. In doing so, particular attention is paid to Hilbert’s axiomatic method and his proposal for the foundations of mathematics, the so-called Hilbert’s program. The book also discusses the development of algebraic number theory, the theory of integral equations, modern algebra and the structural image of mathematics. In addition, it considers the famous list of Mathematical Problems presented in Paris in 1900, the mathematical tradition of the University of Göttingen, the great debate on the foundations of mathematics in the twenties between formalists and intuitionists, and, finally, Hilbert’s work on the theory of relativity and the foundations of quantum mechanics. The book will primarily appeal to an academic audience, although it will also be of interest to general-interest science readers.
Book Synopsis Problems and Solutions in Real Analysis by : Masayoshi Hata
Download or read book Problems and Solutions in Real Analysis written by Masayoshi Hata and published by World Scientific Publishing Company. This book was released on 2016-12-12 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition introduces an additional set of new mathematical problems with their detailed solutions in real analysis. It also provides numerous improved solutions to the existing problems from the previous edition, and includes very useful tips and skills for the readers to master successfully. There are three more chapters that expand further on the topics of Bernoulli numbers, differential equations and metric spaces. Each chapter has a summary of basic points, in which some fundamental definitions and results are prepared. This also contains many brief historical comments for some significant mathematical results in real analysis together with many references. Problems and Solutions in Real Analysis can be treated as a collection of advanced exercises by undergraduate students during or after their courses of calculus and linear algebra. It is also instructive for graduate students who are interested in analytic number theory. Readers will also be able to completely grasp a simple and elementary proof of the Prime Number Theorem through several exercises. This volume is also suitable for non-experts who wish to understand mathematical analysis. Request Inspection Copy Contents:Sequences and LimitsInfinite SeriesContinuous FunctionsDifferentiationIntegrationImproper IntegralsSeries of FunctionsApproximation by PolynomialsConvex FunctionsVarious Proof ζ(2) = π2/6Functions of Several VariablesUniform DistributionRademacher FunctionsLegendre PolynomialsChebyshev PolynomialsGamma FunctionPrime Number TheoremBernoulli NumbersMetric SpacesDifferential Equations Readership: Undergraduates and graduate students in mathematical analysis.
Book Synopsis Derived Langlands: Monomial Resolutions Of Admissible Representations by : Victor P Snaith
Download or read book Derived Langlands: Monomial Resolutions Of Admissible Representations written by Victor P Snaith and published by World Scientific. This book was released on 2018-12-06 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langlands Programme is one of the most important areas in modern pure mathematics. The importance of this volume lies in its potential to recast many aspects of the programme in an entirely new context. For example, the morphisms in the monomial category of a locally p-adic Lie group have a distributional description, due to Bruhat in his thesis. Admissible representations in the programme are often treated via convolution algebras of distributions and representations of Hecke algebras. The monomial embedding, introduced in this book, elegantly fits together these two uses of distribution theory. The author follows up this application by giving the monomial category treatment of the Bernstein Centre, classified by Deligne-Bernstein-Zelevinsky.This book gives a new categorical setting in which to approach well-known topics. Therefore, the context used to explain examples is often the more generally accessible case of representations of finite general linear groups. For example, Galois base-change and epsilon factors for locally p-adic Lie groups are illustrated by the analogous Shintani descent and Kondo-Gauss sums, respectively. General linear groups of local fields are emphasized. However, since the philosophy of this book is essentially that of homotopy theory and algebraic topology, it includes a short appendix showing how the buildings of Bruhat-Tits, sufficient for the general linear group, may be generalised to the tom Dieck spaces (now known as the Baum-Connes spaces) when G is a locally p-adic Lie group.The purpose of this monograph is to describe a functorial embedding of the category of admissible k-representations of a locally profinite topological group G into the derived category of the additive category of the admissible k-monomial module category. Experts in the Langlands Programme may be interested to learn that when G is a locally p-adic Lie group, the monomial category is closely related to the category of topological modules over a sort of enlarged Hecke algebra with generators corresponding to characters on compact open modulo the centre subgroups of G. Having set up this functorial embedding, how the ingredients of the celebrated Langlands Programme adapt to the context of the derived monomial module category is examined. These include automorphic representations, epsilon factors and L-functions, modular forms, Weil-Deligne representations, Galois base change and Hecke operators.
Book Synopsis Smooth-automorphic Forms And Smooth-automorphic Representations by : Harald Grobner
Download or read book Smooth-automorphic Forms And Smooth-automorphic Representations written by Harald Grobner and published by World Scientific. This book was released on 2023-06-09 with total page 262 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a conceptual introduction into the representation theory of local and global groups, with final emphasis on automorphic representations of reductive groups G over number fields F.Our approach to automorphic representations differs from the usual literature: We do not consider 'K-finite' automorphic forms, but we allow a richer class of smooth functions of uniform moderate growth. Contrasting the usual approach, our space of 'smooth-automorphic forms' is intrinsic to the group scheme G/F.This setup also covers the advantage that a perfect representation-theoretical symmetry between the archimedean and non-archimedean places of the number field F is regained, by making the bigger space of smooth-automorphic forms into a proper, continuous representation of the full group of adelic points of G.Graduate students and researchers will find the covered topics appear for the first time in a book, where the theory of smooth-automorphic representations is robustly developed and presented in great detail.
Book Synopsis Introduction to Modern Number Theory by : Yu. I. Manin
Download or read book Introduction to Modern Number Theory written by Yu. I. Manin and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This edition has been called ‘startlingly up-to-date’, and in this corrected second printing you can be sure that it’s even more contemporaneous. It surveys from a unified point of view both the modern state and the trends of continuing development in various branches of number theory. Illuminated by elementary problems, the central ideas of modern theories are laid bare. Some topics covered include non-Abelian generalizations of class field theory, recursive computability and Diophantine equations, zeta- and L-functions. This substantially revised and expanded new edition contains several new sections, such as Wiles' proof of Fermat's Last Theorem, and relevant techniques coming from a synthesis of various theories.
