We study theoretical and practical aspects of high-precision computation of Maass forms. First, we compute to over 1000 decimal places the Laplacian and Hecke eigenval-ues for the first few Maass forms on PSL(2, Z)\H. Second, we give an algorithm for rigorously verifying that a proposed eigenvalue together with a proposed set of Fourier coefficients indeed… (More)
We introduce a new method to bound-torsion in class groups, combining analytic ideas with reflection principles. This gives, in particular, new bounds for the 3-torsion part of class groups in quadratic, cubic and quartic number fields, as well as bounds for certain families of higher degree fields and for higher. Conditionally on GRH, we obtain a… (More)
GPUs and accelerators have become ubiquitous in modern supercomputing systems. Scientific applications from a wide range of fields are being modified to take advantage of their compute power. However, data movement continues to be a critical bottleneck in harnessing the full potential of a GPU. Data in the GPU memory has to be moved into the host memory… (More)
Xeon Phi, based on the Intel Many Integrated Core (MIC) architecture, packs up to 1TFLOPs of performance on a single chip while providing x86__64 compatibility. On the other hand, InfiniBand is one of the most popular choices of interconnect for supercomputing systems. The software stack on Xeon Phi allows processes to directly access an InfiniBand HCA on… (More)
Let G be a split adjoint semisimple group over Q and K∞ ⊂ G(R) a maximal compact subgroup. We shall give a uniform, short and essentially elementary proof of the Weyl law for cusp forms on congruence quotients of G(R)/K∞. This proves a conjecture of Sarnak for Q-split groups, previously known only for the case G = PGL(n). The key idea amounts to a new type… (More)
A ÿnite graph is said to be locally-quasiprimitive relative to a subgroup G of automorphisms if, for all vertices , the stabiliser in G of is quasiprimitive on the set of vertices adjacent to. (A permutation group is said to be quasiprimitive if all of its non-trivial normal subgroups are transitive.) The graph theoretic condition of local quasiprimitivity… (More)
We prove the local-global principle holds for the problem of representations of quadratic forms by quadratic forms, in codimension ≥ 7. The proof uses the ergodic theory of p-adic groups, together with a fairly general observation on the structure of orbits of an arithmetic group acting on integral points of a variety.
We discuss the enumeration of function fields and number fields by discriminant. We show that Malle's conjectures agree with heuristics arising naturally from geometric computations on Hurwitz schemes. These heuristics also suggest further questions in the number field setting.