The authors study Sobolev classes of weakly differentiable mappings $f: {\mathbb X}\rightarrow {\mathbb Y}$ between compact Riemannian manifolds without boundar

The authors prove a general form of the sum formula $\mathrm{SL}_2$ over a totally real number field. This formula relates sums of Kloosterman sums to products

"January 2009, volume 197, number 922 (Fourth of five numbers)."

Consider representation theory associated to symmetric groups, or to Hecke algebras in type A, or to $q$-Schur algebras, or to finite general linear groups in n