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Titlebook: Topics in Number Theory; J. S. Chahal Book 1988 Springer Science+Business Media New York 1988 Finite.Morphism.algebra.calculus.equation.fi

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发表于 2025-3-21 18:03:07 | 显示全部楼层 |阅读模式
书目名称Topics in Number Theory
编辑J. S. Chahal
视频video
丛书名称University Series in Mathematics
图书封面Titlebook: Topics in Number Theory;  J. S. Chahal Book 1988 Springer Science+Business Media New York 1988 Finite.Morphism.algebra.calculus.equation.fi
描述This book reproduces, with minor changes, the notes prepared for a course given at Brigham Young University during the academic year 1984-1985. It is intended to be an introduction to the theory of numbers. The audience consisted largely of undergraduate students with no more background than high school mathematics. The presentation was thus kept as elementary and self-contained as possible. However, because the discussion was, generally, carried far enough to introduce the audience to some areas of current research, the book should also be useful to graduate students. The only prerequisite to reading the book is an interest in and aptitude for mathe­ matics. Though the topics may seem unrelated, the study of diophantine equations has been our main goal. I am indebted to several mathematicians whose published as well as unpublished work has been freely used throughout this book. In particular, the Phillips Lectures at Haverford College given by Professor John T. Tate have been an important source of material for the book. Some parts of Chapter 5 on algebraic curves are, for example, based on these lectures.
出版日期Book 1988
关键词Finite; Morphism; algebra; calculus; equation; finite field; function; mathematics; number theory; theorem
版次1
doihttps://doi.org/10.1007/978-1-4899-0439-3
isbn_softcover978-1-4899-0441-6
isbn_ebook978-1-4899-0439-3
copyrightSpringer Science+Business Media New York 1988
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发表于 2025-3-21 20:29:09 | 显示全部楼层
发表于 2025-3-22 01:29:22 | 显示全部楼层
Algebraic Number Fields,eek the integer solutions of (4.1). If . < 0, these solutions are (±1,0) for . < −1 and (±1,0), (0, ±1) for . = −1. However, if . > 1, it is a nontrivial fact that (4.1) has infinitely many solutions in integers. If we let . denote the set of these solutions, then . has a group structure (cf. Exerci
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Computation of the Mordell-Weil Group,.., .. is of finite order, ..,..., .. cannot be independent. For any elliptic curve . defined over ℚ the group .(ℚ) of rational points on . is finitely generated. The (.) ...(.) of . is defined to be the maximum number of independent elements in .(ℚ). In particular, ..(.) = 0 if and only if .(ℚ) is
发表于 2025-3-22 13:56:05 | 显示全部楼层
Book 1988intended to be an introduction to the theory of numbers. The audience consisted largely of undergraduate students with no more background than high school mathematics. The presentation was thus kept as elementary and self-contained as possible. However, because the discussion was, generally, carried
发表于 2025-3-22 18:27:32 | 显示全部楼层
Basic Properties of the Integers,The most fundamental concept in the study of the integers is that of divisibility.
发表于 2025-3-22 22:39:16 | 显示全部楼层
Algebraic Methods,There are concepts in number theory that are best expressed in the language of algebra. We shall discuss algebra only to the extent needed for our purpose.
发表于 2025-3-23 01:25:30 | 显示全部楼层
Representation of Integers by Forms,The squares (of integers), namely.are very sparse.
发表于 2025-3-23 06:10:30 | 显示全部楼层
Algebraic Curves,So far we have considered only equations of degree at most 2. Because of the group structure on the integer solutions of .. − .. = 1, we were able to employ algebraic methods to find these solutions. Let us now take, as an example, the diophantine equation..
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