Authors: Xiaochun Mei
Four basic problems are found in Riemann’s original paper proposed in 1859. The Riemann hypothesis becomes meaningless. 1. It is proved that on the real axis of complex plane, the Riemann Zeta function equation holds only at point Re(s)=1/2 (s=a+ib) . However, at this point, the Zeta function is infinite, rather than zero. At other points of real axis with a be not equal to zero and b=0 and , the two sides of function equation are contradictory. When one side is finite, another side may be infinite. 2. An integral item around the original point of coordinate system was neglected when Riemann deduced the integral form of Zeta function. The item was convergent when Re(s)>1 but divergent when Re(s)<1. The integral form of Zeta function does not change the divergence of its series form. Two reasons to cause inconsistency and infinite are analyzed. 3. A summation formula was used in the deduction of the integral form of Zeta function. The applicative condition of this formula is x>0. At point x=0 , the formula is meaningless. However, the lower limit of Zeta function’s integral is x=0, so the formula can not be used. 4. The formula of Jacobi function was used to prove the symmetry of Zeta function equation. The applicable condition of this formula is also x>0. Because the lower limit of integral in the deduction was , this formula can not be used too. The zero calculation of Riemann Zeta function is discussed at last. It is pointed out that because approximate methods are used, they are not the real zeros of strict Riemann Zeta function.
Comments: 16 Pages. In Chinese
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[v1] 2024-07-05 16:10:18
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