Local Geometric Proof of Riemann Conjecture
| Autor: | Chuanmiao Chen |
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| Rok vydání: | 2020 |
| Předmět: | |
| Zdroj: | Advances in Pure Mathematics. 10:589-610 |
| ISSN: | 2160-0384 2160-0368 |
| DOI: | 10.4236/apm.2020.1010036 |
| Popis: | Riemann hypothesis (RH) is a difficult problem. So far one doesn’t know how to go about it. Studying ζ and using analysis method likely are two incor-rect guides. Actually, a unique hope may study Riemann function , , by geometric analysis, which has the symmetry: v=0 if β=0, and basic expression . We show that |u| is single peak in each root-interval of u for fixed β ∈(0,1/2]. Using the slope ut, we prove that v has opposite signs at two end-points of Ij. There surely exists an inner point such that , so {|u|,|v|/β} form a local peak-valley structure, and have positive lower bound in Ij. Because each t must lie in some Ij, then ||ξ|| > 0 is valid for any t (i.e. RH is true). Using the positivity of Lagarias (1999), we show the strict monotone for β > β0 ≥ 0 , and the peak-valley structure is equiva-lent to RH, which may be the geometric model expected by Bombieri (2000). This research follows Liuhui’s methodology: “Computing can detect the un-known and method”. |
| Databáze: | OpenAIRE |
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