解析數論-探索整數的結構 (英文) 讓-馬里.德.科寧 9787040612028 【台灣高等教育出版社】
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物品所在地：中國大陸
原出版社：高等教育
物品所在地：中國大陸
原出版社：高等教育
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| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202402*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：解析數論-探索整數的結構 (英文) ISBN：9787040612028 出版社：高等教育 著編譯者：讓-馬里.德.科寧 頁數：414 所在地：中國大陸 *此為代購商品 書號：1625190 可大量預訂，請先連絡。 內容簡介 本書彙集了解析數論中一系列解析數論主題，是解析數論領域的入門讀物，重點關注整數的剖分，即對整數的乘法結構的研究。本書涵蓋了一些最重要的主題，包括算術函數的全局和局部性態、光滑數的廣泛研究等。本書最後還專門講述了整數複合指數的問題。 本書每章末尾都有一系列精心挑選的問題。這些問題可以強化讀者對材料的理解。作者提供了偶數號問題的解答，使得本書非常適合那些想要測試其對書中理論的理解程度的讀者。目錄 PrefaceNotation Frequently Used Functions Chapter 1 Preliminary Notions 1 1 Approximating a sum by an integral 1 2 The Euler-MacLaurin formula 1 3 The Abel summation formula 1 4 Stieltjes integrals 1 5 Slowly oscillating functions 1 6 Combinatorial results 1 7 The Chinese Remainder Theorem 1 8 The density of a set of integers 1 9 The Stirling formula 1 10 Basic inequalities Problems on Chapter 1 Chapter 2 Prime Numbers and Their Properties 2 1 Prime numbers and their polynomial representations 2 2 There exist infinitely many primes 2 3 A first glimpse at the size of π(x) 2 4 Fermat numbers 2 5 A better lower bound for π(x) 2 6 The Chebyshev estimates 2 7 The Bertrand Postulate 2 8 The distance between consecutive primes 2 9 Mersenne primes 2 10 Conjectures on the distribution of prime numbers Problems on Chapter 2 Chapter 3 The Riemann Zeta Function 3 1 The definition of the Riemann Zeta Function 3 2 Extending the Zeta Function to the half-plane σ > 0 3 3 The derivative of the Riemann Zeta Function 3 4 The zeros of the Zeta Function 3 5 Euler's estimate ((2) =π 2/6 Problems on Chapter 3 Chapter 4 Setting the Stage for the Proof of the Prime Number Theorem 4 1 Key functions related to the Prime Number Theorem 4 2 A closer analysis of the functions e(x) and v(x) 4 3 Useful estimates 4 4 The Mertens estimate 4 5 The Mobius function 4 6 The divisor function Problems on Chapter 4 Chapter 5 The Proof of the Prime Number Theorem 5 1 A theorem of D J Newman 5 2 An application of Newman's theorem 5 3 The proof of the Prime Number Theorem 5 4 A review of the proof of the Prime Number Theorem 5 5 The Riemann Hypothesis and the Prime Number Theorem 5 6 Useful estimates involving primes 5 7 Elementary proofs of the Prime Number Theorem Problems on Chapter 5 Chapter 6 The Global Behavior of Arithmetic Functions 6 1 Dirichlet series and arithmetic functions 6 2 The uniqueness of representation of a Dirichlet series Chapter 7 The Local Behavior of Arithmetic Functions Chapter 8 The Fascinating Euler Function Chapter 9 Smooth Numbers Chapter 10 The Hardy-Ramanujan and Landau Theorems Chapter 11 The abc Conjecture and Some of Its Applications Chapter 12 Sieve Methods Chapter 13 Prime Numbers in Arithmetic Progression Chapter 14 Characters and the Dirichlet Theorem Chapter 15 Selected Applications of Primes in Arithmetic Progression Chapter 16 The Index of Composition of an Integer Appendix: Basic Complex Analysis Theory Solutions to Even-Numbered Problems Bibliography Index 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
