When Linnik introduced the classical large-sieve in 1941 [Lin], he was motivated by the
following problem: given a non-trivial primitive character χ modulo q, how large (compared …

The purpose of this semi-expository article is to give another proof of a classical theorem of
Shimura on the critical values of the standard L-function attached to a Hilbert modular form …

Let F be a number field, and let π be a cuspidal, unitary automorphic representation of GL (n,
AF). For almost all finite places v, let Av (π) denote the associated (Langlands) conjugacy …

We obtain resonances for short exponential sums weighted by Fourier coefficients of Maass
forms for SL (n, Z). This involves deriving asymptotics for the integrals appearing in the GL …

We prove that Hermitian cusp forms of weight k for the Hermitian modular group of degree 2
are determined by their Fourier coefficients indexed by matrices whose determinants are …

It is well known that the Tchebotarev density theorem implies that an irreducible ℓ-adic
representation ρ of the absolute Galois group of a number field K is determined (up to …

Let $ K/F $ be a finite Galois extension of number fields. It is well known that the Tchebotarev
density theorem implies that an irreducible, finitely ramified $ p $-adic representation $\rho …

Let $\mathcal {M} _1 $ and $\mathcal {M} _2 $ denote two compact hyperbolic manifolds.
Assume that the multiplicities of eigenvalues of the Laplacian acting on $ L^ 2 (\mathcal {M} …

We obtain a sharp refinement of the strong multiplicity one theorem for the case of unitary
non-dihedral cuspidal automorphic representations for GL (2). Given two unitary cuspidal …

7 From Modular Forms to Automorphic Representations Page 1 7 From Modular Forms to
Automorphic Representations Stephen S. Kudla This chapter sketches the passage from …