Proof of Bernhard Riemann's functional equation using gamma function. Journal of Mathematics and Statistics | July 1, 2008| | COPYRIGHT 2008 Science Publications. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan.  All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information) Copyright

INTRODUCTION

Bernhard Riemann's paper, Ueber die Anzahl der primzahlen unter einer gegebenen Grosse (On the number of primes less than a given quantity) was first published in Monatsberichte de Berliner AKademie, in November 1859. This study, just six manuscript pages in length, introduced radically new idea to the study of prime numbers, ideas which led, in 1896, to independent proofs by Hadamard and de la Vallee Poussin of the prime number theorem. This theorem, first conjectured by Gauss when he was a young man, states that the number of primes less than x is ...

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