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Titlebook: p-adic Numbers; An Introduction Fernando Q. Gouvêa Textbook 19972nd edition Springer-Verlag Berlin Heidelberg 1997 Algebra.absolute values

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書目名稱p-adic Numbers
副標(biāo)題An Introduction
編輯Fernando Q. Gouvêa
視頻videohttp://file.papertrans.cn/765/764605/764605.mp4
概述Includes supplementary material:
叢書名稱Universitext
圖書封面Titlebook: p-adic Numbers; An Introduction Fernando Q. Gouvêa Textbook 19972nd edition Springer-Verlag Berlin Heidelberg 1997 Algebra.absolute values
描述In the course of their undergraduate careers, most mathematics majors see little beyond "standard mathematics:" basic real and complex analysis, ab- stract algebra, some differential geometry, etc. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor- ners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory. This importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. More recently, p-adic num- bers have shown up in other areas of mathematics, and even in physics.
出版日期Textbook 19972nd edition
關(guān)鍵詞Algebra; absolute values on fields; calculus; finite field; number theory; p-adic analysis; p-adic numbers
版次2
doihttps://doi.org/10.1007/978-3-642-59058-0
isbn_ebook978-3-642-59058-0Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer-Verlag Berlin Heidelberg 1997
The information of publication is updating

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Introduction,rners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the .-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis.
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,-adic Numbers,ery hard. Nevertheless, we have preferred to stick, at first, to the most concrete example available. In a later chapter, we will consider some aspects of the problem of extending valuations from ? to larger fields. More details about the theory of valuations on global fields can be found in several of the references.
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Vector Spaces and Field Extensions,lds (for example, when we dealt with the zeros of a function defined by a power series). In fact, just as we have emphasized the natural analogy between the .-adic fields ?. and the field ? of real numbers, it is a very natural thing to do to look for an extension of ?. that is analogous to the comp
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