Riemann's Zeta Function

<p>Bernhard Riemann's eight-page paper entitled On the Number of Primes Less Than a Given Magnitude was a landmark publication of 1859 that directly influenced generations of great mathematicians among them Hadamard Landau Hardy Siegel Jensen Bohr Selberg Artin and Hecke. This text by a noted mathematician and educator examines and amplifies the paper itself and traces the developments in theory inspired by it. (An English translation of the original document appears in the Appendix.)<br>Topics include Riemann's main formula the prime number theorem de la Vallée Poussin's theorem numerical analysis of roots by Euler-Maclaurin summation the Riemann-Siegel formula largescale computations Fourier analysis zeros on the line the Riemann hypothesis and Farey series alternative proof of the integral formula Tauberian theorems Chebyshev's identity and other related topics.<br>This inexpensive edition of Edwards' superb high-level study will be welcomed by students and mathematicians. Mathematically inclined general readers will likewise value this influential classic.</p>