In this paper, we present a truncated version of the classical Fast Fourier Transform. When applied to polynomial multiplication, this algorithm has the nice property of eliminating the jumpss in the complexity at powers of two. When applied to the multiplication of multivariate polynomials or truncated multivariate power series, we gain a logarithmic factor with respect to the best previously ...

A simple and efficient FFT-based fast direct solver for Poisson-type equations on 3D cylindrical and spherical geometries is presented. The solver relies on the truncated Fourier series expansion, where the differential equations of Fourier coefficients are solved using second-order finite difference discretizations without pole conditions. Three different boundary conditions (Dirichlet, Neuman...

The internal and external Robin problems for the Laplace equation in bounded starlike domains are addressed. We show how to derive the relevant solutions by using a suitable Fourier series-like method. Numerical results are specifically obtained considering threedimensional domains whose boundary is defined by a generalization of the so-called ‘‘superformula’’ introduced by Gielis. By using the...

In examining the relationship between the number of points over Fp on certain Calabi-Yau manifolds and hypergeometric series which correspond to a particular period of the manifold, Rodriguez-Villegas identified numerically 22 possible supercongruences. We prove one of the outstanding supercongruence conjectures between a special value of a truncated generalized hypergeometric series and the p-...