| The 'large sieve' is an indispensable tool in modern analytic number theory. A large sieve inequality for a family of arithmetically interesting sequences says that any sequence of complex numbers is orthogonal to the sequences in the family on average. Such inequalities have been established for additive characters, Dirichlet characters, Fourier coefficients of modular forms, to name a few. In this talk, I shall review the theory of modular forms and large sieves and discuss the situation when the sequences are Fourier coefficients of symmetric power lifts of modular forms on GL(2). |