Abstract
After some papers proving the RC (short for “Riemann’s Conjecture”, also known as the “Riemann’s Hypothesis”, RH), now the author provides a new proof, using the “Spira Criterion” that states “The RH is equivalent to the statement that if s>0.5 and t> 6.5 then |z(1-s)|> |z(s)|”. We use the concept of “transfer function” for control systems. This new proof is so simple that the author wonders why a great mathematician like Riemann did not see it; therefore F. Galetto thinks that somewhere in the purported proof there should be an error.
Highlights
It is well known that for over a century mathematicians have been trying to prove the so-called Riemann Hypothesis, RH for short, a conjecture claimed by Riemann [who was professor at University of Gottingen in Germany], near 1859 in a 8-page paper “On the number of primes less than a given magnitude” shown at Berlin Academy, and dated/published in 1859; it is well known, as well, that RH is related to set of all the Prime Numbers (Figure 1); prime numbers are fundamental for encryption of documents and data
If RC would be related to Statistics, , would be confirmed with a Confidence Level (CL) > 0.9999999999: the evidence of 1012 zeros computed, all on the Critical Line supports H0 with that “high” CL
When =0 the “Transfer Function” depends only on the “frequency” ; on we use the symbol s= +j, as it is customary in electronics, communication theory and control systems:
Summary
Applied Science and Innovative Research ISSN 2474-4972 (Print) ISSN 2474-4980 (Online). Fausto Galetto Independent researcher, past professor of Quality Management at Politecnico of Turin, Turin, Italy.
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