{"title":"Ams Ip Studies In Advanced Mathematics","description":null,"products":[{"product_id":"introduction-to-p-adic-analytic-number-theory-book-mram-murty-9780821847749","title":"Introduction to P-adic Analytic Number Theory","description":"This book is an elementary introduction to $p$-adic analysis from the number theory perspective. With over 100 exercises, it will acquaint the non-expert with 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.  The book treats the subject informally, making the text accessible to non-experts. It would make a nice independent text for a course geared toward advanced undergraduates and beginning graduate students.  Titles in this series are co-published with International Press, Cambridge, MA. Table of Contents: Historical introduction; Bernoulli numbers; $p$-adic numbers; Hensel's lemma; $p$-adic interpolation; $p$-adic $L$-functions; $p$-adic integration; Leopoldt's formula for $L_p(1,\\chi)$; Newton polygons; An introduction to Iwasawa theory; Bibliography; Index.  Review from Mathematical Reviews: The exposition of the book is clear and self-contained. It contains numerous exercises and is well-suited for use as a text for an advanced undergraduate or beginning graduate course on $p$-adic numbers and their applications...the author should be congratulated on a concise and readable account of $p$-adic methods, as they apply to the classical theory of cyclotomic fields...heartily recommended as the basis for an introductory course in this area. (AMSIP\/27.S)","brand":"WoB","offers":[{"title":"GB \/ VERY_GOOD \/ INTERNAL","offer_id":49526908256529,"sku":"GOR013607667","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821847740.jpg?v=1751011735"},{"product_id":"lagrangian-intersection-floer-theory-book-kenji-fukaya-9780821852491","title":"Lagrangian Intersection Floer Theory","description":"A co-publication of the AMS and International Press of Boston, Inc.  This is a two-volume series research monograph on the general Lagrangian Floer theory and on the accompanying homological algebra of filtered A?A?-algebras. This book provides the most important step towards a rigorous foundation of the Fukaya category in general context. In Volume I, general deformation theory of the Floer cohomology is developed in both algebraic and geometric contexts. An essentially self-contained homotopy theory of filtered A?A? algebras and A?A? bimodules and applications of their obstruction-deformation theory to the Lagrangian Floer theory are presented. Volume II contains detailed studies of two of the main points of the foundation of the theory: transversality and orientation. The study of transversality is based on the virtual fundamental chain techniques (the theory of Kuranishi structures and their multisections) and chain level intersection theories. A detailed analysis comparing the orientations of the moduli spaces and their fiber products is carried out. A self-contained account of the general theory of Kuranishi structures is also included in the appendix of this volume.","brand":"WoB","offers":[{"title":"US \/ VERY_GOOD \/ SBYB","offer_id":50369677361425,"sku":"CIN0821852493VG","price":0.0,"currency_code":"GBP","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4072\/6801\/files\/0821852493.jpg?v=1750979790"}],"url":"https:\/\/www.worldofbooks.com\/collections\/ams-ip-studies-in-advanced-mathematics-book-series.oembed","provider":"World of Books ","version":"1.0","type":"link"}