Let π be a cuspidal representation on GL(2,AQ). We give nontrivial lower and upper bounds for average of absolute values of Dirichlet coefficients associated to π; and nontrivial upper bound in the case of Sym kπ, k= 2 , 3. These bounds generalize the known estimates in holomorphic case to Maass forms, without assuming the Ramanujan–Petersson conjecture.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Hecke eigenvalues
- Ramanujan–Petersson conjecture
- Symmetric power representations of GL(2)