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Showing 1 to 20 of 40 for “"Fourier coefficients"”.
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Congruence Properties of Fourier Coefficients of Modular Forms
Fourier coefficients of modular forms have profound connections with many areas of number theory. We will consider three different applications of these coefficients. First, we extend the Apery number supercongruence, proving an observation of Rodriguez-Villegas. Second, we prove an analogue of …
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Fourier Coefficients of Modular Forms and Their Applications
The theory of modular forms, as it has been developed over the past several decades, has highlighted deep connections between the areas of analytic and algebraic number theory and arithmetic geometry. In this thesis we explore some applications. First, we give some new and simpler proofs of recent …
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Improved estimation of Fourier coefficients for ill-posed inverse problems
… involves reproducing a function f(x) or its Fourier coefficients from the observed values of the function. The observations of the f(x) are made at n equidistant points on the unit interval with p observations being made at each point. The observations are effected by a random error with a …
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Study of the convergence of series in certain orthogonal functions
… convergence of certain series, in particular a Fourier's series, a Legendre's series, and a series of Bessel's functions. Before proceeding directly to the proof of these theorems, however, we will give some theorems showing the conditions under which the Fourier coefficients in the development …
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Sato-Tate Problem for GL(3)
… a conjectured orthogonality relation between the Fourier coefficients of Maass forms for SL(N,Z) for N≥4, we generalize the above equidistribution theorem to N≥4.
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Time-lapse seismic AVAz in the Stocker Field
… methodologies, namely, Rüger’s method and Fourier Coefficients decomposition method, to address this problem using seismic data targeting the Barnett formation. Rüger’s method uses a linearized version of the full reflection coefficient for HTI media. Fourier Coefficients decomposition …
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A Polynomial Based Iterative Method for Linear Parabolic Equations
… in Chebychev polynomials. The calculation of the Fourier Coefficients requires numerical integration over only a single line segment in the complex plane whose length and orientation depend on the step size and the parabolic operator itself. The simplicity with which these coefficients are …
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Congruences for the Coefficients of Weakly Holomorphic Modular Forms
… of the given arithmetic function appear as the Fourier coefficients of a weakly holomorphic modular form. We show that similar congruences exist for the coefficients of any weakly holomorphic modular form on any congruence subgroup Gamma0(N). In particular, we give congruences for a wide class …
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Flow of [phi] mesons in pPb collisions at the LHC with the CMS detector
… correlations are quantified by the second-order Fourier coefficients (v2) as a function of transverse momentum. The v2 of [phi]-mesons is compared to that of other identified particles, to study the mass ordering and quark number scaling effects in measurements of elliptic flow.
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Higher Siegel-Weil formulae over function fields
… formula in the case of non-degenerate Fourier coefficients, relating the degrees of these cycles to higher derivatives of Siegel-Eisenstein series. In this thesis, we generalize their result in two directions: we 1) prove a higher Siegel-Weil formula for unitary groups for corank-1 …
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Co-rank 1 Arithmetic Siegel--Weil
… first derivatives of unitary Eisenstein series Fourier coefficients. The key input is a new limiting method at all places. On the analytic side, the limit relates local Whittaker functions on different groups. On the geometric side at nonsplit non-Archimedean places, the limit relates degrees of …
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Determination of Mueller matrix elements in the presence of imperfections in optical components
… to determine nine Mueller matrix elements from Fourier analysis of the output signal of a photodetector. The arrangement is modified to the P'PSAA' arrangement where P' and A' represent fixed polarizers that are added at both ends with the speed ratio of the rotating components (P and A) …
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Modified Stochastic Sine-Gordon Equation
… stochastic system (i.e the SDEs of Fourier coefficients related to the SPDE), to control its energy, existence, uniqueness, continuity and stability. The analysis relies on the investigation of expected Lyapunov functional of the energy in terms of all system-parameters. We simulate …
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Numerical detection of complex singularities in two and three dimensions
… In the method, we analyze the decay of Fourier coefficients using a numerical form fit to ascertain the nature of singularities in two and three-dimensional functions. Our results generalize a well known method for the analysis of singularities in one-dimensional functions to higher …
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Fourier analysis on the hypercube, the coefficient problem, and applications
… study some problems that revolve around Fourier analysis. More specifically we focus on the magnitudes of the frequency components. Firstly, we perform a study on the hypercube. It is well known that the Delsarte linear programming bounds provide rich information on the magnitudes of the …
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Estruturas tridimensionais com propriedades mecânicas dos materiais representadas matematicamente por séries - aplicação à análise de pontes
… The mechanical properties are expanded into FOURIER series, allowing for variations in the material and geometric characteristics of the structure. Besides the mechanical properties, all the other dependent variables are also expanded into FOURIER series. As a consequence of the series …
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Congruences in modular, Jacobi, Siegel, and mock modular forms with applications
We study congruences in the coefficients of modular and other automorphic forms. Ramanujan famously found congruences for the partition function like p(5n+4) = 0 mod 5. For a wide class of modular forms, we classify the primes for which there can be analogous congruences in the coefficients of the …
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Computational and Statistical Detection of High-Dimensional Latent Space Structure in Random Networks
… technical ingredient is a strategy for bounding Fourier coefficients of random geometric graphs based on a representation of spherical random geometric graphs as Erdős-Rényi with few planted edges. This part of the thesis is based on [BB24b]. Chapter 3: The conjectured optimality of the signed …
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Two cylindrical vortex sheets : evolution and singularity formation
… Parameters pertaining to the asymptotics of the Fourier coefficients of the vortex sheets' positions are numerically fitted to gain insight into aspects of the singularity formation; these include the order of the branch-point singularities, and the times and locations of singularity formation. A …
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Approximating a wavelet kernel using a quantum computer
… sample plots of 9.09 × 10−9 , by estimating the Fourier coefficients of the kernel. We hope that this can be used as a starting point for performing wavelet analysis on quantum computers.
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