Elementary Modular Iwasawa Theory
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Elementary Modular Iwasawa Theory
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Author : Haruzo Hida
language : en
Publisher: World Scientific
Release Date : 2021-10-04
Elementary Modular Iwasawa Theory written by Haruzo Hida and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-04 with Mathematics categories.
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.
General Financial Awareness Vol 2 Topicwise Notes For All Banking Related Exams A Complete Preparation Book For All Your Banking Exams With Solved Mcqs Ibps Clerk Ibps Po Sbi Po Sbi Clerk Rbi And Other Banking Exams
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Author : EduGorilla Prep Experts
language : en
Publisher: EduGorilla Community Pvt. Ltd.
Release Date : 2023-04-29
General Financial Awareness Vol 2 Topicwise Notes For All Banking Related Exams A Complete Preparation Book For All Your Banking Exams With Solved Mcqs Ibps Clerk Ibps Po Sbi Po Sbi Clerk Rbi And Other Banking Exams written by EduGorilla Prep Experts and has been published by EduGorilla Community Pvt. Ltd. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-29 with Education categories.
EduGorilla's General/Financial Awareness (Vol 2) Study Notes are the best-selling notes for General/Financial Awareness in the English edition. Their content for banking exams is well-researched and covers all topics related to General/Financial Awareness. The notes are designed to help students prepare thoroughly for their exams, with topic-wise notes that are comprehensive and easy to understand. The notes also include solved multiple-choice questions (MCQs) for self-evaluation, allowing students to gauge their progress and identify areas that require further improvement. These study notes are tailored to the latest syllabus of all banking-related exams, making them a valuable resource for exam preparation.
Smooth Automorphic Forms And Smooth Automorphic Representations
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Author : Harald Grobner
language : en
Publisher: World Scientific
Release Date : 2023-06-09
Smooth Automorphic Forms And Smooth Automorphic Representations written by Harald Grobner and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-09 with Mathematics categories.
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.
Elliptic Curves Modular Forms And Iwasawa Theory
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Author : David Loeffler
language : en
Publisher: Springer
Release Date : 2017-01-15
Elliptic Curves Modular Forms And Iwasawa Theory written by David Loeffler and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-15 with Mathematics categories.
Celebrating one of the leading figures in contemporary number theory – John H. Coates – on the occasion of his 70th birthday, this collection of contributions covers a range of topics in number theory, concentrating on the arithmetic of elliptic curves, modular forms, and Galois representations. Several of the contributions in this volume were presented at the conference Elliptic Curves, Modular Forms and Iwasawa Theory, held in honour of the 70th birthday of John Coates in Cambridge, March 25-27, 2015. The main unifying theme is Iwasawa theory, a field that John Coates himself has done much to create. This collection is indispensable reading for researchers in Iwasawa theory, and is interesting and valuable for those in many related fields.
Iwasawa Theory And Its Perspective Volume 2
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Author : Tadashi Ochiai
language : en
Publisher: American Mathematical Society
Release Date : 2024-04-25
Iwasawa Theory And Its Perspective Volume 2 written by Tadashi Ochiai 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 2024-04-25 with Mathematics categories.
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.
Iwasawa Theory 2012
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Author : Thanasis Bouganis
language : en
Publisher: Springer
Release Date : 2014-12-08
Iwasawa Theory 2012 written by Thanasis Bouganis and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-12-08 with Mathematics categories.
This is the fifth conference in a bi-annual series, following conferences in Besancon, Limoges, Irsee and Toronto. The meeting aims to bring together different strands of research in and closely related to the area of Iwasawa theory. During the week before the conference in a kind of summer school a series of preparatory lectures for young mathematicians was provided as an introduction to Iwasawa theory. Iwasawa theory is a modern and powerful branch of number theory and can be traced back to the Japanese mathematician Kenkichi Iwasawa, who introduced the systematic study of Z_p-extensions and p-adic L-functions, concentrating on the case of ideal class groups. Later this would be generalized to elliptic curves. Over the last few decades considerable progress has been made in automorphic Iwasawa theory, e.g. the proof of the Main Conjecture for GL(2) by Kato and Skinner & Urban. Techniques such as Hida’s theory of p-adic modular forms and big Galois representations play a crucial part. Also a noncommutative Iwasawa theory of arbitrary p-adic Lie extensions has been developed. This volume aims to present a snapshot of the state of art of Iwasawa theory as of 2012. In particular it offers an introduction to Iwasawa theory (based on a preparatory course by Chris Wuthrich) and a survey of the proof of Skinner & Urban (based on a lecture course by Xin Wan).
Modular Forms A Classical And Computational Introduction 2nd Edition
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Author : Lloyd James Peter Kilford
language : en
Publisher: World Scientific Publishing Company
Release Date : 2015-03-12
Modular Forms A Classical And Computational Introduction 2nd Edition written by Lloyd James Peter Kilford and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-12 with Mathematics categories.
Modular Forms is a graduate student-level introduction to the classical theory of modular forms and computations involving modular forms, including modular functions and the theory of Hecke operators. It also includes applications of modular forms to various subjects, such as the theory of quadratic forms, the proof of Fermat's Last Theorem and the approximation of π. The text gives a balanced overview of both the theoretical and computational sides of its subject, allowing a variety of courses to be taught from it.This second edition has been revised and updated. New material on the future of modular forms as well as a chapter about longer-form projects for students has also been added.
Hecke S Theory Of Modular Forms And Dirichlet Series
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Author : Bruce C. Berndt
language : en
Publisher: World Scientific
Release Date : 2007
Hecke S Theory Of Modular Forms And Dirichlet Series written by Bruce C. Berndt and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
1. Introduction -- 2. The main correspondence theorem -- 3. A fundamental region -- 4. The case [symbol]> 2 -- 5. The case [symbol]
Elliptic Curves And Arithmetic Invariants
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Author : Haruzo Hida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-13
Elliptic Curves And Arithmetic Invariants written by Haruzo Hida 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 2013-06-13 with Mathematics categories.
This book contains a detailed account of the result of the author's recent Annals paper and JAMS paper on arithmetic invariant, including μ-invariant, L-invariant, and similar topics. This book can be regarded as an introductory text to the author's previous book p-Adic Automorphic Forms on Shimura Varieties. Written as a down-to-earth introduction to Shimura varieties, this text includes many examples and applications of the theory that provide motivation for the reader. Since it is limited to modular curves and the corresponding Shimura varieties, this book is not only a great resource for experts in the field, but it is also accessible to advanced graduate students studying number theory. Key topics include non-triviality of arithmetic invariants and special values of L-functions; elliptic curves over complex and p-adic fields; Hecke algebras; scheme theory; elliptic and modular curves over rings; and Shimura curves.
Elementary Theory Of L Functions And Eisenstein Series
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Author : Haruzo Hida
language : en
Publisher: Cambridge University Press
Release Date : 1993-02-11
Elementary Theory Of L Functions And Eisenstein Series written by Haruzo Hida and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-02-11 with Mathematics categories.
The theory of p-adic and classic modular forms, and the study of arithmetic and p-adic L-functions has proved to be a fruitful area of mathematics over the last decade. Professor Hida has given courses on these topics in the USA, Japan, and in France, and in this book provides the reader with an elementary but detailed insight into the theory of L-functions. The presentation is self contained and concise, and the subject is approached using only basic tools from complex analysis and cohomology theory. Graduate students wishing to know more about L-functions will find that this book offers a unique introduction to this fascinating branch of mathematics.