The aim of this thesis is to provide systematic information on very complicated open problem of mathematics such as the truth of Riemann Hypothesis and the analysis of the Riemann Zeta Function. We know that this problem seems beyond human comprehension and represents rigorous statistical finger print therefore we have to analyze further sources of information for this problem. The accurate direction of development stages for handling this problem is important as well therefore we will analyze the direction of the many problems in light of the renowned mathematician Einstein’s thinking while modeling the ideas for solution. Thesis starts with the earliest writing along with some unknown writing prints of the one of the oldest civilization known as Indus valley civilization and on some development history of mathematics while keeping in touch with the Riemann Zeta function. Thesis consists of five chapters The first chapter reflects the earliest stage of human mind and its ways of modeling the ideas at the earliest stages of the human civilization in Indus Valley Civilization. The second chapter is on certain facts about prime numbers which helps to understand the structures of equations and hence to Random Matrix Theory while the third chapter is on Eigenvalues the very important and ground making branch of mathematics. . (ii) Forth chapter develops the link of field of values, Eigen values & Random Matrix Theory. Fifth chapters suggest collective deeper developments in mathematics to handle open problems of mathematics waiting for solution for more than 150 years.

TITLE - Riemann Zeta Function and Deeper Development in Mathematics
AUTHOR - Shagufta Ahmad
••••••IJSER Edition - November 2013

UNIVERSITY - CMU,where I did independent Research study
GUIDE NAME -
Dr.Ruben Hranti
Dr.Sivaram Narayan