An Unconditional Large Sieve Inequality for L-Functions on GL(n)

Large sieve inequalities provide number theorists with a notion of “quasi-orthogonality” for families of arithmetic objects (Dirichlet characters, elliptic curves, Artin representations, automorphic representations, etc.). Such inequalities are crucial in many averaging problems and can sometimes produce powerful substitutes for the generalized Riemann hypothesis (GRH).

Until now, large sieve inequalities for automorphic representations or Artin representations have relied on progress toward the generalized Ramanujan conjecture or the strong Artin conjecture (respectively). I will discuss a new (and soft) approach to proving large sieve inequalities in which we remove the need for these conjectures. This yields applications to subconvexity for automorphic L-functions and equidistribution of prime splitting behavior in An-fields. This is joint work with Asif Zaman.