Computing to Find Zeros of the Zeta Function

Abstract

Mathematics and computing are closely related. Algorithms and programs are commonly used to solve historic problems or maybe just our homework.

One such example, of the former, is the Euler Equations. These are equations that model the motion of fluids. Everything from a ripple in the puddle of water to designing better airplanes, the equations are used. Euler equations predict how the fluid will evolve for any instant. Although producing precise values for the state of the fluid at any given moment, there may be one of these values which suddenly skyrockets to infinity. At that point, the Euler equations are said to give rise to a “singularity”-or, more radically, to “blow up.”

Computation of the fluid’s flow will no longer be possible.

But how did they reach this conclusion?

Well, through a computer simulation.

Mathematicians think of computers as a vital tool in this age. They are able to calculate any "stubborn" problems. One way of solving the RH is through an investigation of more efficient algorithms and computer programs.

We explore efficient computing methods and changes that can be made to them through two zero-finding, or root-finding, methods used in solving Riemann Hypothesis.