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)**

**-----------**

Real s>1

s=(1/2+

**i**.t)---------------

------------------

**Devoted to Uncle Fotis , my Mentor in Mathematics**

**The easiest proof of the following:**

--------------------

(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