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- GERGELY HARCOS
- 2008

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)

- GERGELY HARCOS
- 2008

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 with unitary central character and contragradi-ent representatioñ π. The approximation involves a smooth truncation of the Dirichlet series L(s, π) and L(s, ˜ π) after about √ C terms,… (More)

Let π 1 , π 2 be cuspidal automorphic representations of PGL 2 (R) of conductor 1 and Hecke eigenvalues λπ 1,2 (n), and let h > 0 be an integer. For any smooth compactly supported weight functions W 1,2 : R × → C and any Y > 0 a spectral decomposition of the shifted convolution sum

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 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) whenever v… (More)

- Imre Bárány, Gergely Harcos, János Pach, Gábor Tardos
- Periodica Mathematica Hungarica
- 2002

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)

- GERGELY HARCOS
- 2008

In the analytic theory of automorphic L-functions one often encounters sums of the form D f (a, b; h) = am±bn=h s(m)t(n)f (am, bn) where a, b, h are positive integers, s(m) and t(n) are the normalized Fourier coefficients of holomorphic or Maass cusp forms coming from automorphic representations of GL(2) over Q and f is some nice weight function on (0, ∞) ×… (More)

- Gergely Harcos
- 2003

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)

- Paul Erdfs, Gergely Harcos, J~nos Pach
- 1998

Let m(n) denote the smallest integer m with the property that any set of n points in Euclidean 3-space has an element such that at most m other elements are equidistant from it. We have that cn 1'3 log log n <<. m(n) <<, n 3/5 fl(n), where c > 0 is a constant and fl(n) is an extremely slowly growing function, related to the inverse of the Ackermann function.

- Lei Wang, Ye-Hua Liu, Mauro Iazzi, Matthias Troyer, Gergely Harcos
- Physical review letters
- 2015

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)