Abstract:
Counting the number of points of an algebraic set over a finite field has been studied by Hasse [1], Lang and Weil [2], and is an important theme in algebra. In this thesis, we present the results found by Chatzidakis, van den Dries and Macintyre in the article Definable Sets over Finite Fields [3] and their applications. These results give estimates of the number of points of definable sets over finite fields. Main theorem of the thesis says that given a formula with n variables, the number of points of the set de ned by this formula in a finite field Fq with q elements is approximately qd. The constants u and d can take only finitely many values independent of the field Fq the formula is defined in.
