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ラーデマッヘル「Lectures on Elementary Number Theory (初等整数論講義)」/平方剰余の相互法則、ガウス和、ディリクレの定理、双子素数
        

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    : 1
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  • Highest Bidder
    : Taka / Rating:33
  • Listing Date
    :2026年03月23日 10時10分
  • Bidding closes on
    :2026年03月29日 22時10分
  • Auction Number
    :o1223869787
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    :Damaged and stained (specify in description)
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Hans Rademacher
「Lectures on Elementary Number Theory」
(ハンス・ラーデマッヘル「初等整数論講義」)

経年並みのヤケシミございますが
書き込み線引きマーカー引き押印等見当たりません

【本書の特徴】
解析と代数の背景を活かし、素因数分解の一意性や平方剰余の相互法則などの基本定理を明確に解説し、巡回論やガウス和、ディリクレの定理、双子素数予想に関するブルンの定理まで扱う点が高く評価されます。
数論学習者の入門書として今も人気があり、簡潔でエレガントな証明が好評です。

【序文からの引用】
この小著は、初等整数論の教科書として企画されたものではない。しかしながら、この分野における予備知識を一切仮定していないという点で、一種の整数論入門書と見なすことができるだろう。
解析学と代数学の基礎を背景として、読者は整数論の主要な定理、すなわち「素因数分解の一意性」と「二次剰余の相互法則」へと導かれる。本書は、いずれの場合も最短で直接的な道筋をたどるものではない。むしろ、数の世界を広く見渡しながら、その背後にある構造を徐々に明らかにしていく方が魅力的に思えたのである。
したがって、素因数分解の一意性は、ファレイ数列に現れる既約分数の構成に関する議論の終わりに登場する。また、二次の相互法則は円分(サイクロトミー)の研究に結びつけられており、その議論はガウスによる正十七角形の作図から始まる。円分の理論はその独自の重要性のため、またガウス和に関する美しい定理の舞台を提供するためにも、ある程度詳細に扱われている。その後、解析的整数論の前奏として漸近的な法則に関する考察がいくつか述べられる。
この書の展開は、等差数列における素数の存在を保証するディリクレの定理と、双子素数に関するV. ブルンの定理によって頂点に達する。
本書の性格はその起源から生じている。すなわち、1959〜1960年にハバーフォード大学でウィリアム・パイル・フィリップス基金の支援を受けて行われた一連の講義を基にしているのである。ただし本書は、その講義をそのまま忠実に再現したものではない。より一貫性を持たせるためにいくつかの内容を再構成し、また他の講義との調和を欠くと思われた分割論の基礎に関する2回分の講義を省いた。さらに、ハバーフォードでの講義には時間の都合で盛り込めなかった最終章を新たに加筆した。この最終章については、後に1960年10月にダートマス大学で講義を行っている。
最後に、講義を本書としてまとめるよう勧めてくれた旧友クレタス・オークリー氏に感謝の意を表したい。また、私の講義ノートを整理してくれたルイス・ソロモン氏、原稿作成を手伝ってくれたジェームズ・O・ブルックス氏にも深く感謝する。
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    Product name: ラーデマッヘル「Lectures on Elementary Number Theory (初等整数論講義)」/平方剰余の相互法則、ガウス和、ディリクレの定理、双子素数
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