Partial fractions and trigonometric identities (Q1296515)

The authors investigate systematically trigonometric summations over the angles equally divided on the upper half plane. A typical example is the sum \(\sum^{n-1}_{k=0} \tan^{2p} ({k\pi\over n})\). For 24 different such sums \(S_p(n)\), they compute the generating function and give the expression of \(S_p(n)\) as a polynomial in \(n\) and \(p\).