Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 20 of 20 for “"Equidistribution"”.
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Sato-Tate Problem for GL(3)
… forms for SL(3,Z), we prove a weighted vertical equidistribution theorem (with respect to the generalized Sato-Tate measure) for the p-th Hecke eigenvalue of Maass forms, with the rate of convergence. With a conjectured orthogonality relation between the Fourier coefficients of Maass forms for …
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Moving mesh methods for solving parabolic partial differential equations
… maintaining the initial distribution amounts to equidistribution. A quantification of the effects of a mesh moving away from an equidistribution are considered here, also the effects of tangling, and then untangling a mesh and restarting.
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Applications of dynamical systems to Farey sequences and continued fractions
… of ergodic theory and dynamical systems to equidistribution and spacing statistics in number theory. The first is concerned with utilizing the ergodic properties of the horocycle flow in SL(2,R) to study the spacing statistics of Farey fractions. For a given finite index subgroup H ⊆ …
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Truncation Error Based Mesh Adaptation and its Application to Multi-Mesh CFD
… approach is compared to the more common equidistribution approach to determine which produces more accurate results as well as the costs associated with each. It is found that the optimization process is able to reduce the truncation error than equidistribution. However, in the 2D cases …
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Some Connections Between Complex Dynamics and Statistical Mechanics
… currents and arithmetic dynamics. We prove a new equidistribution theorem that can be used to relate the chromatic zeros of a hierarchical lattice to the activity current of a particular marked point. We expect that this equidistribution theorem will have several other applications, and describe …
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Fields of rationality of cuspidal automorphic representations
… F in UE/F(n). A key intermediate result is an equidistribution theorem for the local components of families of cuspidal automorphic representations.
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Statistics on pattern-avoiding permutations
… this gives a simple bijective proof of the equidistribution of fixed points in the above two sets of restricted permutations.
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Distribution of Holonomy about Closed Geodesics on Compact Hyperbolic 3-Manifolds
… by their length and holonomy and imply e ective equidistribution of holonomy in shrinking intervals. These theorems result from a non-spherical Selberg's trace formula which relates spectral information to lengths and holonomies of closed geodesics. Then, we show that although holonomy is …
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Dynamic grid adaption using the LPE equation
… cells. To achieve this aim the Laplace Poisson Equidistribution equation is used. Furthermore, the work also covers different types and treatment of weight functions needed to represent areas of high solution activity and a range of techniques necessary to make the use of adaptive grids …
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Dynamical statistics for power series and polynomials with restricted coefficients
… we establish its asymptotics and angular equidistribution. We also prove an anti-concentration inequality for the limit sets, and use this to bound the variation of the number of roots of the typical random power series from its expected value. In the second part, in joint work with Jit Wu …
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Numerical Navier-Stokes solutions of supersonic slot injection problems
… slot injection, an adaptive grid based on the equidistribution law was combined with the solution algorithm. The results from Roe’s FDS method with the adaptive grid showed good results for the supersonic slot injection over a flat plate. For the slot injection over a 10-degree wedge surface …
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Efficient moving mesh methods for Q-tensor models of liquid crystals
… adaptive non-uniform mesh is generated by equidistribution of a selection of strictly positive monitor functions. By an appropriate selection of the monitor function parameters, it is shown that the computed numerical solution converges at an optimal rate with respect to the mesh density …
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The power of random information for numerical approximation and integration
… information in terms of a geometric measure of equidistribution, the distortion, which is well known in the theory of quantization of measures. This holds for isotropic Sobolev as well as Hölder and Triebel-Lizorkin spaces on bounded convex domains. We obtain that for these spaces, depending on …
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THE EFFECTIVE SATO-TATE CONJECTURE AND DENSITIES PERTAINING TO LEHMER-TYPE QUESTIONS
We prove a completely explicit version of the Sato-Tate Conjecture for newforms f(z) on Gamma_0(N) with squarefree level. This result assumes that the symmetric power L-functions of f(z) are automorphic and satisfy the Generalized Riemann Hypothesis. We use this result to compute the density of …
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Verification of Compressible and Incompressible Computational Fluid Dynamics Codes and Residual-based Mesh Adaptation
… For mesh modification, an error equidistribution strategy to perform r-refinement (i.e., mesh node relocation) is employed. This technique is applied to 1D and 2D inviscid flow problems where the exact (i.e., analytic) solution is available. For mesh adaptation based upon TE, …
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An anisotropic adaptive method for the solution of 3-D inviscid and viscous compressible flows
… mesh in the transformed metric space and an equidistribution of the error over the mesh edges. The adaptive strategy can be considered to be the first 3-D implementation of an improved spring analogy-based algorithm originally applied on quadrilateral meshes. The adaptive methodology has been …
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Some topics in analytic and probabilistic number theory
… study of smooth numbers, we will establish an equidistribution result for the y-smooth numbers less than x among arithmetic progressions to modulus q, asymptotically as (logx)/(logq)-+ oo, subject to a certain condition on the relative sizes of y and q. The main point of this work is that it …
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Ranks of tensors and polynomials, with combinatorial applications
… subsets a result of Green and Tao on the equidistribution of high-rank polynomials over finite prime fields. We show that for every fixed prime integer p, for every integer d ∈ [2, p-1], and for every non-empty subset S of F$_{p}$, it is true uniformly in n that if P: F$_{p}^{n}$ → F$_{p}$ …
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Topics in metric geometry, combinatorial geometry, extremal combinatorics and additive combinatorics
… also includes an application of a quantitative equidistribution result for polynomials. In the final part, we consider the Graham-Pollak problem for hypergraphs. Let $f_r(n)$ be the minimum number of complete $r$-partite $r$-graphs needed to partition the edge set of the complete $r$-uniform …
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Effective integrality results in arithmetic dynamics
Given a rational function f defined over a number field K, S. Ih conjectured the finiteness of f-preperiodic points which are S-integral relative to a given non-preperiodic point β. This conjecture remains open, but certain special cases have been proved. We formulate a generalisation of Ih's …