Research
Research in the Mathematical Sciences 2017 4:2
Published on: 10 February 2017
Research
Research in the Mathematical Sciences 2017 4:2
Published on: 10 February 2017
Research
We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e., sums involving a large number of free space Green’s functions. We consider sums involving stokeslets, str...
Research in the Mathematical Sciences 2017 4:1
Published on: 1 February 2017
Research
We study the qualitative homogenization of second-order Hamilton–Jacobi equations in space-time stationary ergodic random environments. Assuming that the Hamiltonian is convex and superquadratic in the momentu...
Research in the Mathematical Sciences 2017 4:6
Published on: 27 January 2017
Research
We consider high-frequency waves satisfying the scalar wave equation with highly oscillatory initial data. The wave speed, and the phase and amplitude of the initial data are assumed to be uncertain, described...
Research in the Mathematical Sciences 2017 4:3
Published on: 24 January 2017
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In this work, we study the convergence of an efficient iterative method, the fast sweeping method (FSM), for numerically solving static convex Hamilton–Jacobi equations. First, we show the convergence of the F...
Research in the Mathematical Sciences 2016 3:35
Published on: 14 December 2016
Research
In this paper, we prove the existence of an infinite-dimensional graded supermodule for the finite sporadic Thompson group Th whose McKay–Thompson series are weakly holomorphic modular forms of weight
Research in the Mathematical Sciences 2016 3:36
Published on: 14 December 2016
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This paper studies algebraic and analytic structures associated with the Lerch zeta function. It defines a family of two-variable Hecke operators
Research in the Mathematical Sciences 2016 3:33
Published on: 12 December 2016
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Research in the Mathematical Sciences 2016 3:31
Published on: 11 December 2016
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We investigate Poincaré series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier ser...
Research in the Mathematical Sciences 2016 3:30
Published on: 10 December 2016
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Research in the Mathematical Sciences 2016 3:32
Published on: 5 December 2016
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In this paper, we provide an explicit construction of weight 0 meromorphic modular forms. Following work of Petersson, we build these via Poincaré series. There are two main aspects of our investigation which ...
Research in the Mathematical Sciences 2016 3:24
Published on: 1 December 2016
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Research in the Mathematical Sciences 2016 3:40
Published on: 14 November 2016
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Research in the Mathematical Sciences 2016 3:41
Published on: 14 November 2016
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We consider the coherent cohomology of toroidal compactifications of locally symmetric varieties (such as Shimura varieties) with coefficients in the canonical and subcanonical extensions of automorphic vector...
Research in the Mathematical Sciences 2016 3:39
Published on: 10 November 2016
Research
Kirwan identified a condition on a smooth function under which the usual techniques of Morse–Bott theory can be applied to this function. We prove that if a function satisfies this condition locally then it al...
Research in the Mathematical Sciences 2016 3:25
Published on: 7 November 2016
Research
We establish asymptotic formulae for the first and second moments of quadratic Dirichlet L-functions, at the center of the critical strip, associated to the real quadratic function field ...
Research in the Mathematical Sciences 2016 3:38
Published on: 2 November 2016
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Dynamical degrees and spectra can serve to distinguish birational automorphism groups of varieties in quantitative, as opposed to only qualitative, ways. We introduce and discuss some properties of those degre...
Research in the Mathematical Sciences 2016 3:23
Published on: 1 November 2016
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We construct the compatible system of l-adic representations associated to a regular algebraic cuspidal automorphic representation of
Research in the Mathematical Sciences 2016 3:37
Published on: 26 October 2016
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Research in the Mathematical Sciences 2016 3:20
Published on: 1 October 2016
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Research in the Mathematical Sciences 2016 3:21
Published on: 1 October 2016
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We show that the Euler system associated with Rankin–Selberg convolutions of modular forms, introduced in our earlier works with Lei and Kings, varies analytically as the modular forms vary in p-adic Coleman fami...
Research in the Mathematical Sciences 2016 3:29
Published on: 1 October 2016
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We construct adic, compactified eigenvarieties parameterizing adic overconvergent Hilbert modular eigenforms of finite slope by constructing integral families of modular sheaves on the relevant formal Shimura ...
Research in the Mathematical Sciences 2016 3:34
Published on: 8 September 2016
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We show that an effective version of Siegel’s theorem on finiteness of integer solutions for a specific algebraic curve and an application of elementary Galois theory are key ingredients in a complexity classi...
Research in the Mathematical Sciences 2016 3:18
Published on: 1 September 2016
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It is well known that time-dependent Hamilton–Jacobi–Isaacs partial differential equations (HJ PDEs) play an important role in analyzing continuous dynamic games and control theory problems. An important tool ...
Research in the Mathematical Sciences 2016 3:19
Published on: 1 September 2016
Research
Research in the Mathematical Sciences 2016 3:28
Published on: 1 September 2016