Gergely Harcos

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Let K be a totally real number field, π an irreducible cuspidal representation of GL2(K)\GL2(AK) with unitary central character, and χ a Hecke character of conductor q. Then L(1/2, π ⊗ χ) ≪ (Nq) 1 2 − 1 8 , where 0 6 θ 6 1/2 is any exponent towards the Ramanujan– Petersson conjecture (θ = 1/9 is admissible). The proof is based on a spectral decomposition of(More)
Let g be a cuspidal newform (holomorphic or Maass) of arbitrary level and nebentypus, w a primitive character of conductor q, and s a point on the critical line <s 1⁄4 12 . It is proved that Lðgn w; sÞfe; g; s q ð1=8Þð1 2yÞþe; where e > 0 is arbitrary and y 1⁄4 7 64 is the current known approximation towards the Ramanujan–Petersson conjecture (which would(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 of radius(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 GLm over a number field. The approximation involves a smooth truncation of the Dirichlet series L(s, π) and L(s, π̃) after about(More)
We present a guiding principle for designing fermionic Hamiltonians and quantum Monte Carlo (QMC) methods that are free from the infamous sign problem by exploiting the Lie groups and Lie algebras that appear naturally in the Monte Carlo weight of fermionic QMC simulations. Specifically, rigorous mathematical constraints on the determinants involving(More)
Let π be a regular algebraic cuspidal automorphic representation of GL2 over an imaginary quadratic number field K, and let ` 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 `-adic representation ρ of Gal(K/K) such that L(s, ρv) = L(s, πv)(More)