Understanding the Xi Function and Symmetry of the Riemann Zeta Function

We discuss the symmetry of the Riemann Zeta Function about the critical line, Re(z) = 1/2. To do this we define a new function which is the product pf the zeta function, the Gamma function, and a power of pi. This xi function will have the property that xi(s) = xi(1-s), which implies the the symmetry of the zeta function. This symmetry provides a clue as to the potential location of zeros of this meromorphic function.

#mikethemathematician, #mikedabkowski, #profdabkowski, #complexanalysis, #riemannzeta