The Riemann Hypothesis Its Origin, Confirmation, Application, and Proof

by H. Vic Dannon

304 pages. Sawn Pictorial Softcover. In his 1859 Zeta paper, Riemann obtained a formula for the count of the primes up to a given number. Riemann’s formula has four terms. But only the first and the third terms have non-negligible values. The first is the dominant term, and can be computed precisely. The third is smaller and depends on the provision that all the zeros of the Zeta function between 0, and 1 are on the line x=1/2 . This provision became known as the Riemann Hypothesis, but it was never hypothesized by Riemann, nor was it used by him. Not seeing an easy proof for it, Riemann used only the first term of his formula and obtained an approximation far superior to Gauss for the count of the primes. We present the Origin, Confirmation, Application, and Proof of the Hypothesis. In the first part, we follow through Riemann’s Zeta paper to trace the origin of the Hypothesis. In the second part, we confirm the Hypothesis with a chi-squared-goodness of fit test of Riemann’s Formula for the Count of the Primes. In the third part, we apply Riemann’s Formula for the Count of the Primes with the Hypothesis Series. In the fourth part, we use results due to Riemann, Weierstrass, Hadamard, and Titchmarsh, to obtain the Hypothesis Proof.

304 pages, Perfect Paperback

Published January 1, 2011