Uploaded March 2019 | Updated September 2026, 2 weeks ago
The full title of this video is On the Riemann Hypothesis, Complex Scalings and Logarithmic Time Reversal
An approach to solve the Riemann Hypothesis is revisited within the framework of the special properties of Θ (theta) functions, and the notion of CT invariance. The conjugation operation C amounts to complex scaling transformations, and the T operation t→(1∕t) amounts to the reversal log(t)→−log(t) . A judicious scaling-like operator is constructed whose spectrum Es=s(1−s) is real-valued, leading to s=12+iρ , and/or s= real. These values are the location of the non-trivial and trivial zeta zeros, respectively. A thorough analysis of the one-to-one correspondence among the zeta zeros, and the orthogonality conditions among pairs of eigenfunctions, reveals that no zeros exist off the critical line. The role of the C,T transformations, and the properties of the Mellin transform of Θ functions were essential in our construction.
Love our work and want more content? Please support our mission, even $1/month helps: quantumgravityresearch.givingcircles.io
VISIT THE QGR WEBSITE: quantumgravityresearch.org
GET TO KNOW QGR’s RESEARCH SCIENTISTS: quantumgravityresearch.org/about-quantum
READ OUR RESEARCH PAPERS & PRESENTATIONS: quantumgravityresearch.org/portfolio/all-papers
QGR FACEBOOK: facebook.com/QuantumGravityResearch
QGR TWITTER: twitter.com/emergencetheory?lang=en
QGR INSTAGRAM: instagram.com/quantumgravityresearch
KLEE IRWIN'S WEBSITE: kleeirwin.com
The full title of this video is On the Riemann Hypothesis, Complex Scalings and Logarithmic Time Reversal
An approach to solve the Riemann Hypothesis is revisited within the framework of the special properties of Θ (theta) functions, and the notion of CT invariance. The conjugation operation C amounts to complex scaling transformations, and the T operation t→(1∕t) amounts to the reversal log(t)→−log(t) . A judicious scaling-like operator is constructed whose spectrum Es=s(1−s) is real-valued, leading to s=12+iρ , and/or s= real. These values are the location of the non-trivial and trivial zeta zeros, respectively. A thorough analysis of the one-to-one correspondence among the zeta zeros, and the orthogonality conditions among pairs of eigenfunctions, reveals that no zeros exist off the critical line. The role of the C,T transformations, and the properties of the Mellin transform of Θ functions were essential in our construction.
Love our work and want more content? Please support our mission, even $1/month helps: quantumgravityresearch.givingcircles.io
VISIT THE QGR WEBSITE: quantumgravityresearch.org
GET TO KNOW QGR’s RESEARCH SCIENTISTS: quantumgravityresearch.org/about-quantum
READ OUR RESEARCH PAPERS & PRESENTATIONS: quantumgravityresearch.org/portfolio/all-papers
QGR FACEBOOK: facebook.com/QuantumGravityResearch
QGR TWITTER: twitter.com/emergencetheory?lang=en
QGR INSTAGRAM: instagram.com/quantumgravityresearch
KLEE IRWIN'S WEBSITE: kleeirwin.com
