Akshay Venkatesh

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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)
We introduce a “geometric” method to bound periods of automorphic forms. The key features of this method are the use of equidistribution results in place of mean value theorems, and the systematic use of mixing and the spectral gap. Applications are given to equidistribution of sparse subsets of horocycles and to equidistribution of CM points; to(More)
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 eigenvalues 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)
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)
Generalizing and unifying prior results, we solve the subconvexity problem for the L-functions of GL1 and GL2 automorphic representations over a fixed number field, uniformly in all aspects. A novel feature of the present method is the softness of our arguments; this is largely due to a consistent use of canonically normalized period relations, such as(More)
A 1nite 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)
The aim of this paper is to use the “amplification technique” to obtain estimates on the dimension of spaces of automorphic forms associated to Galois representations; these bounds improve nontrivially on the work of Duke ([D]). A cuspidal representation π of GL2(AQ) is associated to a 2-dimensional Galois representation ρ : Gal(Q/Q) → GL2(C) if, for each(More)