Rigorous Proof for Riemann Hypothesis Using the Novel Sigma-power Laws and Concepts from the Hybrid Method of Integer Sequence Classification
- John Ting
Abstract
Proposed by Bernhard Riemann in 1859, Riemann hypothesis refers to the famous conjecture explicitly equivalent to the mathematical statement that the critical line in the critical strip of Riemann zeta function is the location for all non-trivial zeros. The Dirichlet eta function is the proxy for Riemann zeta function. We treat and closely analyze both functions as unique mathematical objects looking for key intrinsic properties and behaviors. We discovered our key formula (coined the Sigma-power law) which is based on our key Ratio (coined the Riemann-Dirichlet Ratio). We recognize and propose the Sigma-power laws (in both the Dirichlet and Riemann versions) and the Riemann-Dirichlet Ratio, together with their various underlying mathematically-consistent properties, in providing crucial \textit{de novo} evidences for the most direct, basic and elementary mathematical proof for Riemann hypothesis. This overall proof is succinctly summarized for the reader by the sequential Theorem I to IV in the second paragraph of Introduction section. Concepts from the Hybrid method of Integer Sequence classification are important mathematical tools employed in this paper. We note the intuitively useful mental picture for the idea of the Hybrid integer sequence metaphorically becoming the non-Hybrid integer sequence with certain criteria obtained using Ratio study.- Full Text:
PDF
- DOI:10.5539/jmr.v8n3p9
Journal Metrics
- h-index (December 2021): 22
- i10-index (December 2021): 78
- h5-index (December 2021): N/A
- h5-median (December 2021): N/A
( The data was calculated based on Google Scholar Citations. Click Here to Learn More. )
Index
- Academic Journals Database
- ACNP
- Aerospace Database
- BASE (Bielefeld Academic Search Engine)
- Civil Engineering Abstracts
- CNKI Scholar
- COPAC
- DTU Library
- EconPapers
- Elektronische Zeitschriftenbibliothek (EZB)
- EuroPub Database
- Google Scholar
- Harvard Library
- IDEAS
- Infotrieve
- JournalTOCs
- LOCKSS
- MathGuide
- MathSciNet
- MIAR
- PKP Open Archives Harvester
- Publons
- RePEc
- ResearchGate
- Scilit
- SHERPA/RoMEO
- SocioRePEc
- Standard Periodical Directory
- Technische Informationsbibliothek (TIB)
- The Keepers Registry
- UCR Library
- Universe Digital Library
- WorldCat
Contact
- Sophia WangEditorial Assistant
- jmr@ccsenet.org