Understanding the Zeta function without getting lost in the tricky paths of advanced complex analysis

Scientific Essay from the year 2013 in the subject Mathematics - Number Theory language: English abstract: 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).