Number of points of a nonsingular hypersurface in an odd-dimensional projective space (Q2406697)

The authors consider nonsingular hypersurfaces of degree \(d\geq 2\) in an odd-dimensional projective space over \(\mathbb{F}_q\) in order to generalize their previous results [Finite Fields Appl. 35, 52--60 (2015; Zbl 1330.14035)]. They give an upper bound for the numbers of \(\mathbb{F}_q\)-points of the studied hypersurfaces and the complete list of them that achieve this bound.