## Riemann's Zeta FunctionSuperb high-level study of one of the most influential classics in mathematics examines landmark 1859 publication entitled “On the Number of Primes Less Than a Given Magnitude,” and traces developments in theory inspired by it. Topics include Riemann's main formula, the prime number theorem, the Riemann-Siegel formula, large-scale computations, Fourier analysis, and other related topics. English translation of Riemann's original document appears in the Appendix. |

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if is love for math i swalow it

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I found this book in a small shop in Thailand and bought it on a whim.

Not really knowing anything about the subject, I was still able to follow the arguments of the first 5 chapters.

That made me keen enough to brush up on the background material and re-read it, this time as far as chapter 10 (where googling "adjoint transforms" brought me to this page!)

I like this book enough to bother writing a review of it on my itouch on the beach!

I would recommend it for graduate students and lapsed phd'ers.

### Contents

III | 1 |

IV | 6 |

V | 7 |

VI | 9 |

VII | 11 |

VIII | 12 |

IX | 15 |

X | 16 |

LV | 134 |

LVI | 136 |

LVII | 137 |

LVIII | 141 |

LIX | 145 |

LX | 148 |

LXI | 155 |

LXII | 162 |

XI | 18 |

XII | 20 |

XIII | 22 |

XIV | 23 |

XV | 25 |

XVI | 26 |

XVII | 29 |

XVIII | 31 |

XIX | 33 |

XX | 36 |

XXI | 37 |

XXII | 39 |

XXIII | 40 |

XXIV | 41 |

XXV | 42 |

XXVII | 43 |

XXVIII | 45 |

XXIX | 46 |

XXX | 48 |

XXXI | 50 |

XXXII | 54 |

XXXIII | 56 |

XXXIV | 58 |

XXXV | 61 |

XXXVI | 62 |

XXXVII | 66 |

XXXVIII | 68 |

XXXIX | 70 |

XL | 72 |

XLI | 76 |

XLII | 78 |

XLIII | 79 |

XLIV | 81 |

XLV | 84 |

XLVI | 88 |

XLVII | 91 |

XLVIII | 96 |

XLIX | 98 |

L | 106 |

LI | 114 |

LII | 119 |

LIII | 127 |

LIV | 132 |

LXIII | 164 |

LXIV | 166 |

LXV | 171 |

LXVI | 172 |

LXVII | 175 |

LXVIII | 179 |

LXIX | 182 |

LXX | 183 |

LXXI | 187 |

LXXII | 188 |

LXXIII | 190 |

LXXIV | 193 |

LXXV | 195 |

LXXVI | 199 |

LXXVII | 203 |

LXXVIII | 205 |

LXXIX | 206 |

LXXX | 209 |

LXXXI | 212 |

LXXXII | 213 |

LXXXIII | 215 |

LXXXIV | 216 |

LXXXV | 217 |

LXXXVI | 218 |

LXXXVII | 226 |

LXXXVIII | 229 |

LXXXIX | 237 |

XC | 246 |

XCI | 260 |

XCII | 263 |

XCIII | 268 |

XCIV | 269 |

XCVI | 273 |

XCVII | 278 |

XCVIII | 281 |

XCIX | 284 |

C | 288 |

CI | 298 |

CII | 299 |

CIII | 306 |

311 | |

### Common terms and phrases

absolute convergence adjoint analytic continuation analytic function approaches zero approximation average Backlund bounded Chebyshev circle coefficients computations Consider const constant times log converges decreases defined definite integral denote derivative disk equal Euler product Euler-Maclaurin summation evaluation fact factor Farey series finite number follows functional equation gives Gram points Gram's law halfplane Hardy's theorem hence hypothesis is true implies inequality infinite integrand interval Lehmer lemma less Li(x limit Lindelof's theorem line segment Littlewood log C(j logarithmic logarithmic derivative logx method modulus negative number of roots path of integration polynomial positive real power series preceding section prime number theorem range rapidly real axis real numbers relative error Riemann hypothesis Riemann-Siegel formula right side saddle point Selberg's shown shows Siegel statement Stieltjes Stirling's formula Stirling's series suffices to prove sufficiently large term omitted termwise integration theory tion transform valid zeta function