Local Geometric Proof of Riemann Conjecture
- 1 School of Mathematics and Statistics, Central South University, Changsha, China
- 2 College of Mathematics and Statistics, Hunan Normal University, Changsha, China
Abstract
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 u t , we prove that v has opposite signs at two end-points of I j . There surely exists an inner point such that , so {|u|,|v|/ β } form a local peak-valley structure, and have positive lower bound in I j . Because each t must lie in some I j , 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 > β 0 ≥ 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”.
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