本書適閤數學專業人士和數學愛好者參考閱讀。
本書主要繼承瞭作者本人的劍橋小冊子The Zeta—function of Riemann的內容.本書內容主要包括:ζ(s)函數,狄利剋雷級數與ζ(s)函數的關係,ζ(s)函數的分析特點,函數方程,近似公式,ζ(s)函數在臨界帶的次序.
【目 錄】
Chapter Ⅰ. THE FUNCTIONζ(s) AND THE DIRICHLET SERIES RELATED TO IT//1
Chapter Ⅱ. THE ANALYTIC CHARACTER OFζ(s) AND THE FUNCTIONAL EQATION//13
Chapter Ⅲ. THE THEOREM OF HADAMARD AND DE LA BALIEE POUSSIN AND ITS CONSEQUENCES//46
Chapter Ⅳ. APPROXIMATE FORMULAE//72
Chapter Ⅴ. THE ORDER OFζ(s) IN THE CRITICAL STRIP//98
Chapter Ⅵ. VINOGRADOV’S METHOD//124
Chapter Ⅶ. MEAN-VALUE YHEOREMS//144
Chapter Ⅷ. Ω THEOREMS//192
Chapter Ⅸ. THE GENERAL DISTRIBUTION OF THE ZEROS//221
Chapter Ⅹ. THE ZEROS ON THE CRITICAL LINE//269
Chapter Ⅺ. THE GENERAL DISTRIBUTION OF THE VALUES OFζ(s)//310
Chapter Ⅻ. DIVISOR PROBLEMS//331
Chapter ⅩⅢ. THE LINDELÖF HYPOTHESIS//349
Chapter ⅩⅣ. CONSEQUENCES OF THE RIEMANN HYPOTHESIS//359
Chapter ⅩⅤ. CALCULATIONS RELATING TO THE ZEROS//416
REFERENCES//421
編輯手記//454
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