Advanced Number Theory with Applications (Hardcover)

Richard A. Mollin

  • 出版商: CRC
  • 出版日期: 2009-08-26
  • 售價: $9,070
  • 貴賓價: 9.5$8,617
  • 語言: 英文
  • 頁數: 440
  • 裝訂: Hardcover
  • ISBN: 1420083287
  • ISBN-13: 9781420083286
  • 海外代購書籍(需單獨結帳)

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商品描述

Exploring one of the most dynamic areas of mathematics, Advanced Number Theory with Applications covers a wide range of algebraic, analytic, combinatorial, cryptographic, and geometric aspects of number theory. Written by a recognized leader in algebra and number theory, the book includes a page reference for every citing in the bibliography and more than 1,500 entries in the index so that students can easily cross-reference and find the appropriate data.

With numerous examples throughout, the text begins with coverage of algebraic number theory, binary quadratic forms, Diophantine approximation, arithmetic functions, p-adic analysis, Dirichlet characters, density, and primes in arithmetic progression. It then applies these tools to Diophantine equations, before developing elliptic curves and modular forms. The text also presents an overview of Fermat’s Last Theorem (FLT) and numerous consequences of the ABC conjecture, including Thue–Siegel–Roth theorem, Hall’s conjecture, the Erdös–Mollin-–Walsh conjecture, and the Granville–Langevin Conjecture. In the appendix, the author reviews sieve methods, such as Eratothesenes’, Selberg’s, Linnik’s, and Bombieri’s sieves. He also discusses recent results on gaps between primes and the use of sieves in factoring.

By focusing on salient techniques in number theory, this textbook provides the most up-to-date and comprehensive material for a second course in this field. It prepares students for future study at the graduate level.

商品描述(中文翻譯)

探索數學中最具活力的領域之一,《進階數論與應用》涵蓋了數論的廣泛範疇,包括代數、分析、組合、密碼學和幾何等方面。這本書由一位在代數和數論領域享有盛譽的專家撰寫,書中每一個引用的參考文獻都有頁碼,索引中則有超過1,500個條目,方便學生輕鬆交叉參考並找到相關資料。

本書中包含大量範例,內容首先涵蓋代數數論、二次二元形式、丟番圖逼近、算術函數、p-adic 分析、Dirichlet 字符、密度以及算術級數中的質數。接著,將這些工具應用於丟番圖方程,然後發展橢圓曲線和模形式。文本還概述了費馬最後定理(FLT)及ABC猜想的多個後果,包括Thue–Siegel–Roth定理、Hall猜想、Erdös–Mollin–Walsh猜想和Granville–Langevin猜想。在附錄中,作者回顧了篩法,如厄拉托斯特尼篩、Selberg篩、Linnik篩和Bombieri篩。他還討論了有關質數之間間隙的最新結果以及篩法在因式分解中的應用。

通過專注於數論中的重要技術,這本教科書提供了該領域第二門課程中最新和最全面的材料,為學生未來的研究生學習做好準備。