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Iwasawa Theory And Its Perspective Volume 1 Tadashi Ochiai

Name: Iwasawa Theory And Its Perspective Volume 1 Tadashi Ochiai
SKU: BELL-50261518
Price: 31.00 USD
Availability: InStock
Rating: 5 (70 reviews)

SKU: BELL-50261518

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Iwasawa Theory And Its Perspective Volume 1 Tadashi Ochiai instant download after payment.

Publisher: American Mathematical Society

File Extension: PDF

File size: 3.17 MB

Pages: 154

Author: Tadashi Ochiai

ISBN: 9781470456726, 1470456729

Language: English

Year: 2023

Product desciption

Iwasawa Theory And Its Perspective Volume 1 Tadashi Ochiai by Tadashi Ochiai 9781470456726, 1470456729 instant download after payment.

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 of this book is an update of the classical theory for class groups taking into account the changed point of view on Iwasawa theory. The goal of this first part of the two-part publication is to explain the theory of ideal class groups, including its algebraic aspect (the Iwasawa class number formula), its analytic aspect (Leopoldt–Kubota $L$-functions), and the Iwasawa main conjecture, which is a bridge between the algebraic and the analytic aspects. The second part of the book will be published as a separate volume in the same series, Mathematical Surveys and Monographs of the American Mathematical Society.