ZETA Function_Enoch_O_O ignorance of Mathematical Basics

by Fausto Galetto

From December 15 2016 up to March 30 2017 I have been reading papers uploaded in Academia.edu byOpeyemi Enoch; I wrote several documents, uploaded in Academia.edu, showing the many and many errorsof Opeyemi Enoch. They are many more than thos\e I showed.The last of my documents is given here to show that Enoch Opeyemi Oluwole Department of Mathematics,Federal University Oye-Ekiti, Ekiti State, Nigeria does not know the Basics of Mathematics.

There is no hope that Enoch Opeyemi Oluwole Department of Mathematics stopspublishing rubbish on the Zeta Function...He seems not to realize that it was already proved that there are infinite non-trivialzeros on the Critical Line, but infinite does not mean ′′′ALL non-trivial zeros are onthe Critical Line′′′............

Enoch Opeyemi Oluwole does not care about scientificness...

Fausto Galetto April 2 2017

=========================================================================

March 30 2017, time 8.56

NEW MONADE of Enoch on the ZETA FunctionCOMMENTS by Fausto Galetto

AbstractFausto Galetto just downloaded from Academia.edu (March 30 2017) a new set of MONADE of Enoch!!!I got the message Opeyemi Enoch just uploaded a paper: Obtaining the Riemann Zeta Function From itszeros: An Elementary Proof of the Riemann Hypothesis

Opeyemi Enoch Federal University,Oye-Ekiti, Mathematics Science, Faculty Member

On March 31 2017 I GOT THE SAME MESSAGE!!!! WHY????????????It is really amazing that Enoch Opeyemi Oluwole Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria does not know the Basics of Mathematics and makes the same errors paperafter paper. He cannot deal with the series of complex variables and with basic knowledge of Algebra. Asusual Enoch Opeyemi Oluwole does not care about scientificness.

COMMENTS by Fausto Galetto on the paper

Obtaining the Riemann Zeta Function From its zeros: An Elementary Proof of the Riemann HypothesisEnoch Opeyemi Oluwole Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria

As usual Enoch Opeyemi Oluwole does not care about scientificness

He writes

′′It is an established fact that the Riemann Zeta Function has three classes of roots, namely;

.

′′

Why THREE???????????????

0.5 + i t and 0.5 + i t are in different classes????????????

∑ −2����� is NOT a class!!!!!!!!!!!!!! IT IS a divergent series!!!

How many NONsenses are in two rows????????????????

′′The author (Enoch Opeyemi Oluwole!!!) seeks to proof the Riemann Hypothesis by showing thatif the Riemann Zeta function can be derived from its zeros then, one can proof that all the non-trivial zeros will always have their real parts 0.5 as since the zeros are unique and that the zerosof the analytic continuation formula will always be real.′′

REAL??? ONLY -2n, for n=1, 2, ..., ∞ are real.

NOTICE the NONSENSE:

IF z1 and z2 are any two of the infinite zeros THEN ′′′′the multiplication of these zeros′′′′ is a complexnumber z1z2!!!! [a basic knowledge of Algebra shows that!!!]

IF z1, z2, z3, ...., zn are any n-tuple of the infinite zeros THEN ′′′′the multiplication of these zeros′′′′ is acomplex number z1z2z3.... zn!!!! [for any n; a basic knowledge of Algebra shows that!!!]

THEREFORE it is FALSE the Enoch Opeyemi Oluwole statement ′′′′The Riemann Zeta Function is

derived from the multiplication of these zeros′′′′!!!!

The Riemann Zeta Function is a complex FUNCTION NOT a complex number!!!

NOTICE the CONTRADICTION (of Enoch Opeyemi Oluwole):

THEN Enoch Opeyemi Oluwole goes on writing

At this point Enoch Opeyemi Oluwole proves his ignorance about mathematicalseries by saying

DO YOU SEE in (11) the Enoch Opeyemi Oluwole ignorance about mathematicalseries???

MATHEMATICS does not allows to write a single seriesas a product of two series

� �

�

���

= � ����(���)

�

���

= �� ���

�

���

� �� �(���)

�

���

� ∗∗∗

This is the SAME TYPE of ERROR made by Enoch Opeyemi Oluwole in a previouspaper which I commented few days ago!!! (see Appendix for details)

The Derivation of The Riemann Zeta Function from Euler’s Quadratic Equation And The Proof ofThe Riemann Hypothesis

Enoch Opeyemi Oluwole Department of Mathematics, Federal University Oye-Ekiti Ekiti State, Nigeria

FROM

��2� + �

2�

�

���

� �2�

(� − 1)� ��[��� − �� − �(�)]

�

���

�

YOU CANNOT derive

�� �2�

(� − 1)�

2� + �

2�[��� − �� − �(�)]

�

���

�

From the wrong formula

� �

�

���

= � ����(���)

�

���

= �� ���

�

���

� �� �(���)

�

���

� ∗∗∗

one can derive that the NONSENSE

� �

�

���

= z(�)z(−� − �) DDD

for z=0 ζ(0) ζ(-1)= [-0.5] [-1/12]=1/24and NOT ∞ [as per DDD]!!!

It is useless going onwith the other errors...Fausto Galetto========================================================================Appendix [March 17 2017, time 16.56]

The Derivation of The Riemann Zeta Function from Euler’s Quadratic EquationAnd The Proof of The Riemann Hypothesis

Enoch Opeyemi OluwoleDepartment of Mathematics, Federal University Oye-Ekiti

Ekiti State, Nigeria

The Author in his works [15,16][15] O. O. Enoch (2015): The Eigenvalues (Energy Levels) of the Riemann Zeta function InternationalScientific Journal. Journal of Mathematics. Vol. 1. 2015.www.scientific-journal.com[16] O. O. Enoch (2016): The Proof of the Riemann Hypothesis. International Scientific Journal. Journal ofMathematics. Vol. 2. 2016. www.scientific-journal.com.

has shown that the Meromorphic functions that are equivalent to the Riemann zeta function are given as

NOTICE the part in between

THERE IS NO NEED of the boxed part to go from (9) to (10)!!!!!Enoch Opeyemi Oluwole, Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria

DOES NOT KNOW Mathematics, because HE consider equivalent theformulae (11) and (12): the same symbol ζE(z) CANNOT be used fordifferent functions!!!!!!!!!!!!!

Enoch Opeyemi Oluwole, Department of Mathematics, Federal University Oye-Ekiti, Ekiti State, Nigeria

DOES NOT KNOW Mathematics, because HE consider equivalent theformulae (13) and (14)!!!!!!!!!!!!!

As a matter of fact from 14, written as

��

2Γ(

�

2)� �

2�

(� − 1)� ��[��� − �� − �(�)]

�

���

� =

= ��2� + �

2�

�

���

� �2�

(� − 1)� ��[��� − �� − �(�)]

�

���

� =

= �2�

(� − 1)� ��

2� + �

2�

�

���

� ��[��� − �� − �(�)]

�

���

� ∗∗∗

YOU CANNOT derive

�� �2�

(� − 1)�

2� + �

2�[��� − �� − �(�)]

�

���

�

that is

IF ONE put z=0 in the formula

�2�

(� − 1)� ��

2� + �

2�

�

���

� ��[��� − �� − �(�)]

�

���

� ∗∗∗

HE GETS

{−2�} �� 1

�

���

� ��[�(�)]

�

���

�

AND NOT -0.5=[ζ(0)]

I doubt about the statement of Enoch Opeyemi Oluwole, Department of Mathematics, Federal UniversityOye-Ekiti, Ekiti State, Nigeria

Fausto Galetto

Enoch Opeyemi Oluwole,Department of Mathematics, Federal University Oye-Ekiti, Ekiti

State, NigeriaNEVER considered what I wrote in Academia.edu

Fausto Galetto