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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)
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)
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)
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.
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)