Five Mistakes in Riemann’s Original Paper in 1859 Made Riemann Hypothesis Meaningless
The original paper proposed by Riemann in 1859 has five main errors. The Riemann hypothesis is rendered useless. 1. When the left-hand side of an equation is finite on the real axis of the complex plane and in the domain of the function, the right-hand side may be infinite, and vice versa. Only at Re(s) = 1/2(s= a+) does the Riemann Zeta function equation hold. However, because the Zeta function is infinite rather than 0 at this time, the Riemann hypothesis is invalidated. 2. When Riemann determined the integral form of the Zeta function, an integral item surrounding the initial point of coordinate system was neglected. When Re(s) > 1, the item was convergent, but when Re(s) 1, it was divergent. The Zeta function does not have an integral form adjust the series form’s divergence 3. The integral form of the Zeta function was deduced using a summation technique. This formula’s applicative condition is x > 0. The formula is nonsensical for point x = 0. However, because the integral of the Zeta function has a lower bound of x = 0, the formula cannot be utilised. 4. The integrand function is not uniformly convergent since the integral lower limit of the Zeta function is zero, therefore the integral and sum signs cannot be swapped. However, Riemann rendered them convertible, making the integral version of the Zeta function unworkable. 5.The symmetry of the Zeta function equation was demonstrated using the Jacobi function formula. This formula’s relevant condition is also x > 0 . This formula cannot be applied since the lowest limit of integral in the deduction was x = 0. Finally, the Riemann Zeta function’s zero calculation is addressed. The analytic quality of the original function is destroyed as a result of the employment of approximation techniques, and the Cauchy-Riemann equation cannot be fulfilled. As a result, they are not the rigorous Riemann Zeta function’s real zeros.
Department of Theoretical Physics and Pure Mathematics, Institute of Innovative Physics in Fuzhou, China..