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本橋洋一「整数論基礎講義」
        

  • Product Quantity
    : 1
  • Starting Bid
    :1,000円
  • Highest Bidder
    : タカ / Rating:699
  • Listing Date
    :2026年03月10日 20時34分
  • Bidding closes on
    :2026年03月15日 22時34分
  • Auction Number
    :x1222454065
  • Condition
    :State it in the description
  • Automatic Extension
    :Yes
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    :No
  • Early Closing
    :Yes
  • Can I return the product?
    :no
  • Description
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本橋洋一「整数論基礎講義」
書き込み線引きマーカー引き等ありません。

以下、著者から読者へのコメントを抜粋します。
【目的】
整数論のごく基礎的かつ伝統的な部面を独習を旨とし講述する。大まかには、互除法がその本来の意味を保つ乗法的事象の範囲内に止まる。分野を分かつことは意味無きことではあるが、強いて言うなれば、解析的整数論の初歩に関わるところにやや力点を置く。一方、代数的整数論に関わるところはあえて本講義の外にあるものとし、必要に応じ導入的な言及をする。よって、語り得ぬこと多量。しかしながら、この制約内にありつつも語り得ること語るべきこともまた多量。取捨選択を避け得ず。とくに思いを残すところは、有限体上の曲線に関する議論の割愛、余りの容量超過を避けるがゆえである。

【読み方】
全96節は註も含め通読を旨として編まれている。演習問題を付きず。しかし、しばしば推論・数値計算の一部を補うことを行間の課題とする。

【予備知識】
講義のほぼ全般に渡り初等算術のみを手段とする。しかし、ときとして線形代数、群環体、類別、準同型のごく初歩を最小限度用いる。これらの概念が必然として誕生したことを示唆することも本講義の目的の一つである。たしかに、群論の言葉を全面的に用いるならば、講述ははるかに整理整頓される。しかし、まずは整数論の里を愛でるべし。代数学を学ぶに当たり、軽数論の基礎事項につき初期の証明法を手中にしておくことも肝要。
また、複素変数函数をごく限られた場面にて援用する。解析接続も整数論における一必然。

【最近の進展】
素数分布論、因数分解法などにつき目覚ましい成果が次々と現れつつある、取り分け、算法の提起,改良は非常な速度をもって行われている。本講義および先行自著
YM (2009,2011)の主目的は、それら進展の理解に資する基本的素養の講述である。つまり、現代の敏な算法の個々につき特段の解説は行わない。もちろん、何れが何れの新展開に深く関わるのか、根本の着想は如何なるものか、示唆的な記述は試みる。数学における跳躍の常ながら、何れの着想も至極単純である。本講義内にて典型例は量子計算による因数分解理論(§§49-50).その数学的内容はDirichlet の時代にも優に理解されたかに映る。根底的かつ具体に徹した素養が如何に重要であるかを甚く語るものである。
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    Product name: 本橋洋一「整数論基礎講義」
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