We establish an asymptotic formula for the weighted quantum variance of dihedral Maass forms on Γ 0 </...

After reviewing the group structure and representation theory for dihedral $$D_{2n},$$ we consider an intertwining operator $$\varPhi _\rho $$ from algebra $$\mathbb {C}[D_{2n}]$$ into a corresponding space of semi-magic matrices. From this operator, one obtains generating function enumerating associated squares with fixed line sum extending circulant While work complements approach to $$D_{2n}...

Let ? be a simple undirected graph on finite vertex set and let A its adjacency matrix. Then is singular if singular. The problem of characterizing graphs easy to state but very difficult resolve in any generality. In this paper we investigate the singularity for which dihedral group acts transitively vertices as automorphisms.

Abstract It is known that secure computation can be done by using a deck of physical cards. This area called card-based cryptography. Shinagawa et al. (in: Provable security—9th international conference, ProvSec 2015, Kanazawa, Japan, 2015) proposed regular n -sided polygon cards enable to compute functions over $${\mathbb {Z}}/n{\mathbb {Z}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/M...