本书主要继承了作者本人的剑桥小册子The Zeta—function of Riemann的内容.本书内容主要包括：ζ(s)函数，狄利克雷级数与ζ(s)函数的关系，ζ(s)函数的分析特点，函数方程，近似公式，ζ(s)函数在临界带的次序.
本书适合数学专业人士和数学爱好者参考阅读.
【目 录】
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 LINDELOF HYPOTHESIS//349
Chapter ⅩⅣ. CONSEQUENCES OF THE RIEMANN HYPOTHESIS//359
Chapter ⅩⅤ. CALCULATIONS RELATING TO THE ZEROS//416
REFERENCES//421
编辑手记//454
