Sentence examples for roots of unity from inspiring English sources

Also included is a study of the roots of unity.

Furthermore, their coefficients are multiplicative up to roots of unity, generalizing the notion of Euler products.

These sinusoids are generated by the th roots of unity in the complex plane.

A key ingredient in the method is the tight frame property of the roots of unity.

Since is initially only defined over the roots of unity in the plane, while is defined over roots of unity, we define for by ideal bandlimited interpolation (specifically time-limited spectral interpolation in this case).

It therefore can be used to determine all of the th roots of unity (see §3.12 above).

The sampled sinusoids generated by integer powers of the roots of unity are plotted in Fig.6.2.

In the easiest case, one obtains a transparent formulation by means of roots of unity, which are special values of exponential functions.

The use of trigonometric functions to express components is introduced next, and the roots of unity are discovered by surprisingly laborious means.

The research here is based on the structure of vanishing sums of roots of unity, and is closely related to the problem of spectral self-affine measure.

The GPV invariants take the form of power series converging in the unit disk, and whose radial limits at the roots of unity give the Witten-Reshetikhin-Turaev invariants.