Download or read book Iwasawa Theory and Its Perspective Volume 2 written by Tadashi Ochiai and published by American Mathematical Society. This book was released on 2024-04-25 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iwasawa theory began in the late 1950s with a series of papers by Kenkichi Iwasawa on ideal class groups in the cyclotomic tower of number fields and their relation to $p$-adic $L$-functions. The theory was later generalized by putting it in the context of elliptic curves and modular forms. The main motivation for writing this book was the need for a total perspective of Iwasawa theory that includes the new trends of generalized Iwasawa theory. Another motivation is to update the classical theory for class groups, taking into account the changed point of view on Iwasawa theory. The goal of this second part of the three-part publication is to explain various aspects of the cyclotomic Iwasawa theory of $p$-adic Galois representations.
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.
Download or read book Automorphic Forms Beyond mathrm GL 2 written by Ellen Elizabeth Eischen and published by American Mathematical Society. This book was released on 2024-03-26 with total page 199 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Langlands program has been a very active and central field in mathematics ever since its conception over 50 years ago. It connects number theory, representation theory and arithmetic geometry, and other fields in a profound way. There are nevertheless very few expository accounts beyond the GL(2) case. This book features expository accounts of several topics on automorphic forms on higher rank groups, including rationality questions on unitary group, theta lifts and their applications to Arthur's conjectures, quaternionic modular forms, and automorphic forms over functions fields and their applications to inverse Galois problems. It is based on the lecture notes prepared for the twenty-fifth Arizona Winter School on “Automorphic Forms beyond GL(2)”, held March 5–9, 2022, at the University of Arizona in Tucson. The speakers were Ellen Eischen, Wee Teck Gan, Aaron Pollack, and Zhiwei Yun. The exposition of the book is in a style accessible to students entering the field. Advanced graduate students as well as researchers will find this a valuable introduction to various important and very active research areas.
Download or read book Modern Kaluza Klein Theories written by Thomas Appelquist and published by Addison Wesley Publishing Company. This book was released on 1987 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive and impressive collection of original and translated papers by Kaluza, Klein, Einstein and others, carefully edited to place them in their historical and intellectual context.
Download or read book Number Theory written by Kazuya Kato and published by American Mathematical Soc.. This book was released on 2000 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Renormalization and Effective Field Theory written by Kevin Costello and published by American Mathematical Soc.. This book was released on 2011 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quantum field theory has had a profound influence on mathematics, and on geometry in particular. However, the notorious difficulties of renormalization have made quantum field theory very inaccessible for mathematicians. This provides complete mathematical foundations for the theory of perturbative quantum field theory, based on Wilson's ideas of low-energy effective field theory and on the Batalin-Vilkovisky formalism.
Download or read book Linear Groups written by Leonard Eugene Dickson and published by . This book was released on 1901 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Group Theory and Three Dimensional Manifolds written by John R. Stallings and published by . This book was released on 1971 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book New Industrial Spaces written by Allen John Scott and published by . This book was released on 1988 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Number Theory 1 written by Kazuya Kato and published by American Mathematical Soc.. This book was released on 2000 with total page 180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the English translation of the original Japanese book. In this volume, "Fermat's Dream", core theories in modern number theory are introduced. Developments are given in elliptic curves, $p$-adic numbers, the $\zeta$-function, and the number fields. This work presents an elegant perspective on the wonder of numbers. Number Theory 2 on class field theory, and Number Theory 3 on Iwasawa theory and the theory of modular forms, are forthcoming in the series.
Download or read book Fairbairn s Object Relations Theory in the Clinical Setting written by David P. Celani and published by Columbia University Press. This book was released on 2010 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: W. R. D. Fairbairn (1889-1964) challenged the dominance of Freud's drive theory with a psychoanalytic theory based on the internalization of human relationships. Fairbairn assumed that the unconscious develops in childhood and contains dissociated memories of parental neglect, insensitivity, and outright abuse that are impossible the children to tolerate consciously. In Fairbairn's model, these dissociated memories protect developing children from recognizing how badly they are being treated and allow them to remain attached even to physically abusive parents. Attachment is paramount in Fairbairn's model, as he recognized that children are absolutely and unconditionally dependent on their parents. Kidnapped children who remain attached to their abusive captors despite opportunities to escape illustrate this intense dependency, even into adolescence. At the heart of Fairbairn's model is a structural theory that organizes actual relational events into three self-and-object pairs: one conscious pair (the central ego, which relates exclusively to the ideal object in the external world) and two mostly unconscious pairs (the child's antilibidinal ego, which relates exclusively to the rejecting parts of the object, and the child's libidinal ego, which relates exclusively to the exciting parts of the object). The two dissociated self-and-object pairs remain in the unconscious but can emerge and suddenly take over the individual's central ego. When they emerge, the "other" is misperceived as either an exciting or a rejecting object, thus turning these internal structures into a source of transferences and reenactments. Fairbairn's central defense mechanism, splitting, is the fast shift from central ego dominance to either the libidinal ego or the antilibidinal ego-a near perfect model of the borderline personality disorder. In this book, David Celani reviews Fairbairn's five foundational papers and outlines their application in the clinical setting. He discusses the four unconscious structures and offers the clinician concrete suggestions on how to recognize and respond to them effectively in the heat of the clinical interview. Incorporating decades of experience into his analysis, Celani emphasizes the internalization of the therapist as a new "good" object and devotes entire sections to the treatment of histrionic, obsessive, and borderline personality disorders.
Download or read book Number Theory written by Kazuya Kato and published by . This book was released on 2000 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Attractors Under Autonomous and Non autonomous Perturbations written by Matheus C. Bortolan and published by American Mathematical Soc.. This book was released on 2020-05-29 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive study of how attractors behave under perturbations for both autonomous and non-autonomous problems. Furthermore, the forward asymptotics of non-autonomous dynamical systems is presented here for the first time in a unified manner. When modelling real world phenomena imprecisions are unavoidable. On the other hand, it is paramount that mathematical models reflect the modelled phenomenon, in spite of unimportant neglectable influences discounted by simplifications, small errors introduced by empirical laws or measurements, among others. The authors deal with this issue by investigating the permanence of dynamical structures and continuity properties of the attractor. This is done in both the autonomous (time independent) and non-autonomous (time dependent) framework in four distinct levels of approximation: the upper semicontinuity, lower semicontinuity, topological structural stability and geometrical structural stability. This book is aimed at graduate students and researchers interested in dissipative dynamical systems and stability theory, and requires only a basic background in metric spaces, functional analysis and, for the applications, techniques of ordinary and partial differential equations.
Download or read book Introduction to p adic Analytic Number Theory written by M. Ram Murty and published by American Mathematical Soc.. This book was released on 2009-02-09 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises included, it will acquaint the non-expert to the basic ideas of the theory and encourage the novice to enter this fertile field of research. The main focus of the book is the study of $p$-adic $L$-functions and their analytic properties. It begins with a basic introduction to Bernoulli numbers and continues with establishing the Kummer congruences. These congruences are then used to construct the $p$-adic analog of the Riemann zeta function and $p$-adic analogs of Dirichlet's $L$-functions. Featured is a chapter on how to apply the theory of Newton polygons to determine Galois groups of polynomials over the rational number field. As motivation for further study, the final chapter introduces Iwasawa theory.
Download or read book Line Diagrams for Logic written by George Englebretsen and published by Edwin Mellen Press. This book was released on 1998 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents a number of reasons for the reinstatement of a traditional terminist logic, contributing to the ongoing debate concerning the proper connections between formal logic, natural language, artificial reasoning, and mathematics.
Download or read book Books in Series written by and published by . This book was released on 1985 with total page 1404 pages. Available in PDF, EPUB and Kindle. Book excerpt: Vols. for 1980- issued in three parts: Series, Authors, and Titles.
Download or read book Schaum s Outline of Theory and Problems of Development Economics written by Dominick Salvatore and published by McGraw-Hill Companies. This book was released on 1977 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
