ERGODICITY OF A CLASS OF COCYCLES OVER IRRATIONAL ROTATIONS

It is proved that if alpha is irrational and phi is-an-element-of L2(S1) with phi(n) is-an-element-of .(1/n) then for each m is-an-element-of Z\{0} the corresponding skew product (e2piix, e2piiy) bar arrow pointing right (e2pii(x+alpha), e2pii(phi(x)+mx+y) is ergodic. The rigidity of special flows over irrational rotations with roof functions whose Fourier coefficients are in .(1/n) is also shown.