Bulletin of the
Korean Mathematical Society BKMS

Given a function on a scheme over a finite field, we can count the number of rational points of the scheme having the same values. We show that if the function, viewed as a morphism to the affine line, is proper and its higher direct image sheaves are tamely ramified at the infinity then the values are uniformly distributed up to some degree.

Keywords: distribution, values of functions, finite fields

MSC numbers: 11T23, 11G25, 14G15