For strongly Euler-homogeneous, Saito-holonomic, and tame analytic germs, we consider general types of multivariate Bernstein–Sato ideals associated to arbitrary factorizations our germ. We show that these are principal, the zero loci different related by a diagonal property. If, additionally, divisor is hyperplane arrangement, obtain nice estimates for locus its ideal attached factorization in...

This paper proposes new factorizations for computing the Neumann series. The factorizations are based on fast algorithms for small prime sizes series and the splitting of large sizes into several smaller ones. We propose a different basis for factorizations other than the well-known binary and ternary basis. We show that is possible to reduce the overall complexity for the usual binary decompos...

A recently developed PLUS factorization holds great promise in image coding due to its simplicity and integer reversibility. However, existing PLUS factorizations did not consider stability and optimality. To address these problems, we propose methodologies to design stable and optimal PLUS factorization algorithms. Firstly, we propose three stable PLUS factorization algorithms, prove the stabi...

A factorization theory is proposed for Wiener-Hopf plus Hankel operators with almost periodic Fourier symbols. We introduce a factorization concept for the almost periodic Fourier symbols such that the properties of the factors will allow corresponding operator factorizations. Conditions for left, right, or both-sided invertibility of the Wiener-Hopf plus Hankel operators are therefore obtained...

Consider factorizations into transpositions of an n-cycle in the symmetric group Sn. To every such factorization we assign a monomial in variables wij that retains the transpositions used, but forgets their order. Summing over all possible factorizations of n-cycles we obtain a polynomial that happens to admit a closed expression. From this expression we deduce a formula for the number of 1-fac...

Let T N,χ p,k (x) be the characteristic polynomial of the Hecke operator T p acting on the space of cusp forms S k (N, χ). We describe the factorization of T N,χ p,k (x) mod as k varies, and we explicitly calculate those factorizations for N = 1 and small. These factorizations are used to deduce the irreducibility of certain T 1,1 q,k (x) from the irreducibility of T 1,1 2,k (x).

The number of shortest factorizations into reflections for a Singer cycle in GLn(Fq) is shown to be (qn − 1)n−1. Formulas counting factorizations of any length, and counting those with reflections of fixed conjugacy classes are also given. The method is a standard character-theory technique, requiring the compilation of irreducible character values for Singer cycles, semisimple reflections, and...

Let T N; p;k (x) be the characteristic polynomial of the Hecke operator Tp acting on the space of cusp forms Sk(N; ). We describe the factorization of T N; p;k (x) mod ` as k varies, and we explicitly calculate those factorizations for N = 1 and small `. These factorizations are used to deduce the irreducibility of certain T 1;1 q;k (x) from the irreducibility of T 1;1 2;k (x).

Let V be a vector space endowed with non-degenerate quadratic form Q. If the base field F is different from F2, it known that every isometry can written as product of reflections. In this article, we detail structure poset all minimal length reflection factorizations an isometry. ordered field, also study into positive reflections, i.e., reflections defined by vectors norm. We characterize such...