Ramanujan's Lost Notebook: Part V
暫譯: 拉馬努金的失落筆記：第五部分

George E. Andrews, Bruce C. Berndt

Ramanujan's Lost Notebook: Part V
  • 出版商: Springer
  • 出版日期: 2018-09-18
  • 售價: $6,360
  • 貴賓價: 9.5 折 $6,042
  • 語言: 英文
  • 頁數: 430
  • 裝訂: Hardcover
  • ISBN: 3319778323
  • ISBN-13: 9783319778327

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商品描述

In the spring of 1976, George Andrews of Pennsylvania State University visited the library at Trinity College, Cambridge, to examine the papers of the late G.N. Watson. Among these papers, Andrews discovered a sheaf of 138 pages in the handwriting of Srinivasa Ramanujan. This manuscript was soon designated, "Ramanujan's lost notebook." Its discovery has frequently been deemed the mathematical equivalent of finding Beethoven's tenth symphony.

This fifth and final installment of the authors’ examination of Ramanujan’s lost notebook focuses on the mock theta functions first introduced in Ramanujan’s famous Last Letter. This volume proves all of the assertions about mock theta functions in the lost notebook and in the Last Letter, particularly the celebrated mock theta conjectures. Other topics feature Ramanujan’s many elegant Euler products and the remaining entries on continued fractions not discussed in the preceding volumes. 

Review from the second volume:
"Fans of Ramanujan's mathematics are sure to be delighted by this book. While some of the content is taken directly from published papers, most chapters contain new material and some previously published proofs have been improved. Many entries are just begging for further study and will undoubtedly be inspiring research for decades to come. The next installment in this series is eagerly awaited."
- MathSciNet

Review from the first volume:
"Andrews and Berndt are to be congratulated on the job they are doing. This is the first step...on the way to an understanding of the work of the genius Ramanujan. It should act as an inspiration to future generations of mathematicians to tackle a job that will never be complete."
- Gazette of the Australian Mathematical Society

商品描述(中文翻譯)

在1976年春季，來自賓夕法尼亞州立大學的喬治·安德魯斯（George Andrews）造訪劍橋大學的三一學院圖書館，檢查已故G.N.沃森（G.N. Watson）的文件。在這些文件中，安德魯斯發現了一捆138頁的手稿，這是斯里尼瓦薩·拉馬努金（Srinivasa Ramanujan）的手寫稿。這份手稿很快被指定為「拉馬努金的失落筆記本」。其發現經常被認為是數學界相當於發現貝多芬的第十交響曲。

這本書的第五和最後一部分，專注於拉馬努金在其著名的《最後信件》中首次介紹的模擬θ函數（mock theta functions）。本卷證明了失落筆記本和《最後信件》中關於模擬θ函數的所有主張，特別是著名的模擬θ猜想（mock theta conjectures）。其他主題包括拉馬努金的多個優雅的歐拉乘積（Euler products）以及在前幾卷中未討論的連分數（continued fractions）剩餘條目。

第二卷的評論：
「拉馬努金數學的粉絲們一定會對這本書感到高興。雖然部分內容直接取自已發表的論文，但大多數章節包含新材料，並且一些先前發表的證明得到了改進。許多條目都渴望進一步研究，無疑將在未來幾十年中激發研究靈感。這個系列的下一部分令人期待。」
- MathSciNet

第一卷的評論：
「安德魯斯和伯恩特（Berndt）值得祝賀他們所做的工作。這是理解天才拉馬努金工作的第一步……應該能激勵未來的數學家們去挑戰一項永遠無法完成的工作。」
- 澳洲數學學會公報（Gazette of the Australian Mathematical Society）

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