Gergely Harcos

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Acknowledgments To begin, I want to thank my advisor, Fernando Rodriguez-Villegas, for helpful discussions and encouragement during the last three years. I owe much to my friend and collaborator Jim Kelliher for his patience while listening to me explain my ideas, and Misha Vishik for his constant encouragement. I benefited from the advice and suggestions(More)
Let K be a totally real number field, π an irreducible cuspidal representation of GL 2 (K)\ GL 2 (A K) with unitary central character, and χ a Hecke character of conductor q. Then L(1/2, π ⊗ χ) ≪ (N q) 1 2 − 1 8 (1−2θ)+ε , where 0 θ 1/2 is any exponent towards the Ramanujan– Petersson conjecture (θ = 1/9 is admissible). The proof is based on a spectral(More)
Let π be a regular algebraic cuspidal automorphic representation of GL 2 over an imaginary quadratic number field K, and let ℓ be a prime number. Assuming the central character of π is invariant under the non-trivial automorphism of K, it is shown that there is a continuous irreducible ℓ-adic representation ρ of Gal(K/K) such that L(s, ρv) = L(s, πv)(More)
We find tight estimates for the minimum number of proper subspaces needed to cover all lattice points in an n-dimensional convex body C, symmetric about the origin 0. This enables us to prove the following statement, which settles a problem of G. Halász. The maximum number of n-wise linearly independent lattice points in the n-dimensional ball rB n of(More)
This dissertation contributes to the analytic theory of automorphic L-functions. We prove an approximate functional equation for the central value of the L-series attached to an irreducible cuspidal automorphic representation π of GL m over a number field. The approximation involves a smooth truncation of the Dirichlet series L(s, π) and L(s, ˜ π) after(More)