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Christof Born: The secret of Ishango
Even if we do not always agree on some mathematical formulations, I think that Christof Born has nevertheless written an exciting, number-mystical essay! Book: The Secret of Ishango
Download CD for the book
Important note: The third, revised edition of the book “prime numbers – things long-known and things new-found” is now available in bookstores. The enclosed CD can now be downloaded in compliance with the terms of use in the download area. The abridged book can be read as PDF or online.
(Inverse) Riemann spectrum shows resonances at prime numbers
Here is a comprehensive description of the topic in the last two posts about the sum formula. It is already well-known as the “Riemann spectrum of prime numbers”. The authors are Geoffrey Glover, Grant Keane and Rita Post. Link: https://people.uwec.edu/mbirika/M395_Riemann/The_Riemann_Spectrum_of_the_Prime_Numbers.pdf
Plot of the Inverse Riemann spectrum: resonances of prime numbers
Here is a plot of the Inverse Riemann Spektrum in the range 10 – 100. The first 2000 zeros of Riemann’s Zeta-function have been evaluated. Prime numbers and their powers have been marked on the x-axis (big / small red circles). For Zooming into the picture please click on it.
Sum formula shows nice resonances at primes and prime powers
The following sum formula which shows very impressive peaks at the positions of primes and their powers. The formula displays the ‘Inverse Riemann spectrum’ of the non trivial roots of the zeta function: Here the sum goes over the imaginary parts of the non trivial zeros of Riemanns Zeta function, taking nmax zeros. The…