Realizing that the study of Zeta function ~(s) is dependent on the Gamma function I(s) , a function that I know well for s=x ER, I decided to search for the Zeta function in the internet ie: to get an overall satisfactory idea about the Zeta function ~(s) s=(o+i.t).
General remarks on the Zeta function (s)
And the first 42 roots in the critical strip
Understanding the Riemann Zeta function
And the Riemann Hypothesis
X(s)=X(1-s) Analytic Continuation
Notice that: (1/2 + i.t) = (1/2 - i.t)
For further details see also the pdf by Theodore Yoder
An Introduction to Riemann Hypothesis
The proof that:
(pdf by T.Yoder)
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Real s>1
s=(1/2+i.t)
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Devoted to Uncle Fotis , my Mentor in Mathematics
The easiest proof of the following:
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(1/2 + i.t) = (1/2 i.t )
Roots in the above range: 30.424876126 32.935061588
37.58617815 40.918719012 43.327073281
48.005150881 49.773832478
Remarks about analytic continuation
See also the pdf by Lorenzo Menici
for the complete proof of the above
Some additional remarks on the Zeta function
Exclusively for the members of the top club
of Prime Numbers Theorem
Summary of the Riemann Hypothesis
(1/2 + i.t) = (1/2 i.t)
Excerpt out of 34 pages
- scroll top
- Quote paper
- Prof. Dr. med. John Bredakis (Author), 2013, Understanding the Zeta function, without getting lost in the tricky paths of advanced complex analysis, Munich, GRIN Verlag, https://www.hausarbeiten.de/document/207998
Look inside the ebook
