Can You Hear the Shape of a Curve?
Abstract: The zeta function of a curve over a finite field encodes the number of points on that curve. How much information does the zeta function of a curve plus the zeta function of natural covers give about a curve? This is analogous to the famous question “Can You Hear The Shape of a Drum?” I’ll discuss several versions of this question and an application to factoring polynomials over finite fields.