An Introduction to Probabilistic Number Theory

Kowalski, Emmanuel

  • 出版商: Cambridge
  • 出版日期: 2021-05-06
  • 售價: $2,040
  • 貴賓價: 9.8$1,999
  • 語言: 英文
  • 頁數: 250
  • 裝訂: Hardcover - also called cloth, retail trade, or trade
  • ISBN: 1108840965
  • ISBN-13: 9781108840965
  • 相關分類: 機率統計學 Probability-and-statistics
  • 立即出貨 (庫存=1)

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商品描述

Despite its seemingly deterministic nature, the study of whole numbers, especially prime numbers, has many interactions with probability theory, the theory of random processes and events. This surprising connection was first discovered around 1920, but in recent years the links have become much deeper and better understood. Aimed at beginning graduate students, this textbook is the first to explain some of the most modern parts of the story. Such topics include the Chebychev bias, universality of the Riemann zeta function, exponential sums and the bewitching shapes known as Kloosterman paths. Emphasis is given throughout to probabilistic ideas in the arguments, not just the final statements, and the focus is on key examples over technicalities. The book develops probabilistic number theory from scratch, with short appendices summarizing the most important background results from number theory, analysis and probability, making it a readable and incisive introduction to this beautiful area of mathematics.

商品描述(中文翻譯)

儘管整數的研究,特別是質數的研究,看似具有確定性,但它與概率理論、隨機過程和事件理論有著許多交互作用。這種令人驚訝的聯繫最早於1920年左右被發現,但近年來這些聯繫變得更加深入和更好地理解。本教科書針對初級研究生,首次解釋了這個故事中一些最現代的部分。這些主題包括切比雪夫偏差、黎曼默奇函數的普遍性、指數和被稱為克魯斯特曼路徑的迷人形狀。全書強調在論證中的概率思想,而不僅僅是最終陳述,並且重點放在關鍵示例上,而非技術性細節。本書從頭開始發展概率數論,並附有簡短的附錄,概述了數論、分析和概率中最重要的背景結果,使其成為這個美麗數學領域的可讀且深入的介紹。