In this work we present an explicit relation between the number of points on
a family of algebraic curves over \F_{q} and sums of values of certain
hypergeometric functions over \F_{q}. Moreover, we show that these
hypergeometric functions can be explicitly related to the roots of the zeta
function of the curve over \F_{q} in some particular cases. A general
conjecture relating these last two is presented and advances toward its proof
are shown in the last section.Comment: 24 page
