Let \(\textit{K}\) be a cubic number field. In this paper, we study the Ramanujan sums \(c_{\mathcal {J}}(\mathcal {I})\), where \(\mathcal {I}\) and {J}\) are integral ideals in {O}_\textit{K}\). The asymptotic behaviour of {I})\) over both is investigated.

An r-uniform hypergraph H consists of a set vertices V and edges whose elements are r-subsets V. We define hypertree to be connected which contains no cycles. A spans if it is subhypergraph all H. Greenhill et al. (2017) gave an asymptotic formula for the average number spanning trees in graphs with given, sparse degree sequence. prove analogous result hypergraphs given sequence k=(k1,…,kn). Ou...