The Cheers The Cheers The Cheers were an American vocal group, that had a string of hits in the mid-1950s starting with "(Bazoom) I Need Your Lovin'." which hit number three on the U.S. chart in 1954. This was the first hit written by Jerry Leiber and Mike Stoller to chart on the pop charts in the United States, and was one of the first rock and roll hits by a white group (after The Crew Cuts and Bill Haley and the Comets). The following year, they followed it with "Black Denim Trousers and Motorcycle Boots" (also written by Leiber and Stoller),
Weil pairing on the "n"-torsion. The Weil pairing does not extend to a pairing on all the torsion points (the direct limit of "n"-torsion points) because the pairings for different "n" are not the same. However they do fit together to give a pairing "T"("E") × "T"("E") → "T"(μ) on the Tate module "T"("E") of the elliptic curve "E" (the inverse limit of the ℓ-torsion points) to the Tate module "T"(μ) of the multiplicative group (the inverse limit of ℓ roots of unity). For abelian varieties over an algebraically closed field "K", the Weil pairing is a nondegenerate pairing for all "n"