Spectrum of the Burnside Tambara functor on a cyclic $p$-group

For a finite group $G$, a Tambara functor on $G$ is regarded as a $G$-bivariant analog of a commutative ring. In this analogy, previously we have defined an ideal of a Tambara functor. In this article, we will demonstrate a calculation of the prime spectrum of the Burnside Tambara functor, when $G$ is a cyclic $p$-group for a prime integer $p$.