INSEAD Library

Includes bibliographical references and index

Digitized

Prime Obsession Bernhard Riemann and the Greatest Unsolved Problem in Mathematics Contents Prologue ............................................................................................. ix Part I The Prime Number Theorem 1 Card Trick ....................................................................................... 3 2 The Soil, the Crop ......................................................................... 19 3 The Prime Number Theorem ........................................................ 32 4 On the Shoulders of Giants ........................................................... 48 5 Riemann's Zeta Function .............................................................. 63 6 The Great Fusion .......................................................................... 82 7 The Golden Key, and an Improved Prime Number Theorem ........................................................ 99 8 Not Altogether Unworthy ........................................................... 118 9 Domain Stretching ...................................................................... 137 10 A Proof and a Turning Point ..................................................... 151 Part II The Riemann Hypothesis 11 Nine Zulu Queens Ruled China ................................................ 169 12 Hilbert's Eighth Problem ........................................................... 184 13 The Argument Ant and the Value Ant ...................................... 201 14 In the Grip of an Obsession ....................................................... 223 15 Big Oh and MObius Mu ............................................................ 238 16 Climbing the Critical Line ........................................................ 252 17 A Little Algebra ........................................................................ 265 18 Number Theory Meets Quantum Mechanics ............................ 280 19 Turning the Golden Key............................................................. 296 20 The Riemann Operator and Other Approaches ......................... 312 21 The Error Term ......................................................................... 327 22 Either It's True, or Else It Isn't .................................................. 350 Epilogue ......................................................................................... 362 Notes ............................................................................................... 365 Appendix: The Riemann Hypothesis in Song ................................ 393 Picture Credits ................................................................................ 405 Index ............................................................................................... 407