1206.6673 (Noureddine Chair)

Trigonometrical sums connected with one-dimensional lattice, the chiral
Potts model, and number theory using the residue operator    [PDF]

Noureddine Chair

We have recently developed a method for obtaining exact two-point resistance on the square $N$-cycle, the complete graph minus $N$ edges of the opposite vertices, here, a similar method is used to obtain closed formulas of certain trigonometrical sums that arise in connection with one-dimensional lattice and the chiral Potts model. By modifying slightly, the previous computations, then, we are able to get new closed formulas for different trigonometrical sums, some of which appear in number theory.

View original: http://arxiv.org/abs/1206.6673