In this paper we study absolutely summing mappings on Banach spaces by exploring the cotype of their domains and ranges. It is proved that every n-linear mapping from L∞-spaces into K is (2; 2, ..., 2,∞)-summing and also shown that every n-linear mapping from L∞-spaces into F is (q; 2, ..., 2)-summing whenever F has cotype q. We also give new examples of analytic summing mappings and polynomial...

In this paper we estimate sums of the form $$\sum _{n\le X}|a_{{\text {Sym}}^m \pi }(|f(n)|)|$$ , for symmetric power lifts automorphic representations $$\pi $$ attached to holomorphic forms and polynomials $$f(x)\in {\mathbb {Z}}[x]$$ arbitrary degree. We give new upper bounds these under certain natural assumptions on f. Our results are unconditional when $$\deg (f)\le 4$$ . Moreover, study a...