Dickman, Benjamin M. Uploaded Files

Abstract: This thesis concerns the number of zeros of a multivariable polynomial f over a finite field. More specifically, the zeta-function of f is defined in terms of a certain power series with coefficients determined by the number of zeros of f over various finite fields. Our main result is Dwork's Theorem, stating that the zeta-function of f is in fact a rational function, i.e., a quotient of two polynomials, each with rational coefficients.