Number Theory And The Regularisation Of The Zeta Function

Abstract

The zeta function is employed in theoretical mathematics and physics. Regularization, which can be used to characterize the antecedents and traces of specific self-adjoint operators, is a sort of sum ability or normalization that provides finite values to diverging sums or products. The goal is to figure out what ill-conditioned sums in number theory mean and how important Zeta Function Regularisation is. The role of number theory in the zeta function is studied, and the zeta function is made more regular. This is used a lot to solve problems in physics. The result is that applying the technique of analytic extension via the zeta function necessitates a significant amount of mathematical work. This shouldn't be a surprise that has been linked to so many mistakes and accidents.