Definition:Distance to Nearest Integer Function/Definition 1

Definition

The nearest integer function $\norm \cdot: \R \to \closedint 0 {\dfrac 1 2}$ is defined as:

$\norm \alpha:= \min \set {\size {n - \alpha}: n \in \Z}$

Also see

• Equivalence of Definitions of Distance to Nearest Integer Function

Sources

• 1991: S.W. Graham and G. Kolesnik: Van der Corput's Method of Exponential Sums