We consider the question of the correlation of Fourier coefficients of modular forms with functions of algebraic origin. We establish the absence of correlation in considerable generality (with a power saving of Burgess type) and a corresponding equidistribution property for twisted Hecke orbits. This is done by exploiting the amplification method and the Riemann Hypothesis over finite fields, ...

In this study we have examined a plane wave diffraction problem by a finite plate having different impedance boundaries. The Fourier transforms were used to reduce the governing problem into simultaneous Wiener-Hopf equations which are then solved using the standard Wiener-Hopf procedure. Afterwards the separated and interacted fields were developed asymptotically by using inverse Fourier trans...

The bottleneck of micromagnetic simulations is the computation of the long-ranged magnetostatic fields. This can be tackled on regular N-node grids with Fast Fourier Transforms in time N logN , whereas the geometrically more versatile finite element methods (FEM) are bounded to N in the best case. We report the implementation of a Non-uniform Fast Fourier Transform algorithm which brings a N lo...

A dual algorithm for problems of Fourier Synthesis is proposed. Partially finite convex programming provides tools for a formulation which enables to elude static pixelization of the object to be reconstructed. This leads to a regularized reconstruction-interpolation formula for problems in which finitely many and possibly irregularly spaced samples of the Fourier transform of the unknown objec...

The problem of several finite moving cracks in a functionally graded material is solved by dislocation technique under the condition of anti-plane deformation. By using the Fourier transform the stress fields are obtained for a functionally graded strip containing a screw dislocation. The stress components reveal the familiar Cauchy singularity at the location of dislocation. The solution is em...

Pure and Applied Mathematics—Two Sides of a Coin In November of 1979 there appeared in the Bulletin of the AMS a paper by L. Auslander and R. Tolimieri [3] with the delightful title “Is Computing with the Finite Fourier Transform Pure or Applied Mathematics?” This rhetorical question was answered by showing that in fact the finite Fourier transform and the family of efficient algorithms used to...

Conventional Fourier analysis has many schemes for different types of signals. They are Fourier transform (FT), Fourier series (FS), discrete-time Fourier transform (DTFT), and discrete Fourier transform (DFT). The goal of this correspondence is to develop two absent schemes of fractional Fourier analysis methods. The proposed methods are fractional Fourier series (FRFS) and discrete-time fract...