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 >
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”.