A New Approach to Non-Local Boundary Value Problem for the Cauchy-Riemann Equation | Chapter 10 | Research Updates in Mathematics and Computer Science Vol. 1

 We present an approach to inverstigation of the solutions of the boundary value problem for the Cauchy-Riemann equation on the curvelinear strip in the real plane. Here the boundary conditions are in the special type and are fundamental with respect to the direction solutions are used. As a result, an analytic form of the solution of considered boundary value problem is obtained.

Author(s) Details:

Nihan A. Aliyev,
Baku State University, 23 Zahid Khalilov Street, Baku AZ1148, Republic of Azerbaijan.

Alexander A. Katz,
Department of Mathematics & Computer Science, St. John’s College of LAS, St. John’s University, 8000 Utopia Parkway, SJH-334-G, Queens, NY 11439, USA.

Metanet B. Mursalova,
Baku State University, 23 Zahid Khalilov Street, Baku AZ1148, Republic of Azerbaijan.

Please see the link here: https://stm.bookpi.org/RUMCS-V1/article/view/13677

A Strict Proof That the Riemann Zeta Function Equation Has No Non-trivial Zeros | Chapter 07 | Novel Research Aspects in Mathematical and Computer Science Vol. 2

 On the full complex plain, a standard approach is presented to verify that the Riemann Zeta function equation contains no non-trivial zeros. The Riemann Zeta function equation's real and imaginary parts are totally separated. A set of equations regarding a and b is derived by comparing the real and imaginary halves of the Zeta function equation separately. It is demonstrated that this equation set only contains trivial zero solutions. The only method to get potential non-trivial zeros is for and to be equal to zero at the same time. However, it is demonstrated that and cannot be equal to 0 at the same time using the compassion technique of infinite series. So there are no non-trivial solutions to the Riemann Zeta function equation.

Author(S) Details

Mei Xiaochun
Department of Theoretical Physics and Pure Mathematics, Institute of Innovative Physics in Fuzhou, China..

View Book:- https://stm.bookpi.org/NRAMCS-V2/article/view/6793

Five Mistakes in Riemann’s Original Paper in 1859 Made Riemann Hypothesis Meaningless | Chapter 06 | Novel Research Aspects in Mathematical and Computer Science Vol. 2

 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.

Author(S) Details

Mei Xiaochun
Department of Theoretical Physics and Pure Mathematics, Institute of Innovative Physics in Fuzhou, China..

View Book:- https://stm.bookpi.org/NRAMCS-V2/article/view/6792