X iv :1 00 8. 50 35 v1 [ m at h. N T ] 3 0 A ug 2 01 0 RECOVERING FOURIER COEFFICIENTS OF MODULAR FORMS AND FACTORING OF INTEGERS Sergei N. Preobrazhenskĭi It is shown that if a function defined on the segment [−1, 1] has sufficiently good approximation by partial sums of the Legendre polynomial expansion, then, given the function’s Fourier coefficients cn for some subset of n ∈ [n1, n2], one c...

We take advantage of different generalizations of the tangent manifold to the context of graded manifolds, together with the notion of super section along a morphism of graded manifolds, to obtain intrinsic definitions of the main objects in supermechanics such as, the vertical endomorphism, the canonical and the Cartan’s graded forms, the total time derivative operator and the super–Legendre t...

We introduce a new join operation on colored simplicial complexes that preserves the CohenMacaulay property. An example of this operation puts the connection between the central Delannoy numbers and Legendre polynomials in a wider context. Résumé. Nous introduisons une nouvelle opération qui joint des complexes simpliciaux équilibrés d’une telle manière que la propriété de Cohen-Macaulay est pr...

Exact and approximate analytical solutions of linear and nonlinear singular two-point boundary value problems (BVPs) are obtained for the first time by the Legendre operational matrix of differentiation. Different from other numerical techniques, shifted Legendre polynomials and their properties are employed for deriving a general procedure for forming this matrix. The accuracy of the technique...