Let Tp,k(x) be the characteristic polynomial of the Hecke operator Tp acting on the space of level 1 cusp forms Sk(1). We show that Tp,k(x) is irreducible and has full Galois group...
In this paper, we study p-divisibility of discriminants of Hecke algebras associated to spaces of cusp forms of prime level. By considering cusp forms of weight bigger than 2, we a...
We present a Monte Carlo algorithm for testing multivariate polynomial identities over any field using fewer random bits than other methods. To test if a polynomial P(x1 ::: xn) ...
We introduce the concept of comprehensive triangular decomposition (CTD) for a parametric polynomial system F with coefficients in a field. In broad words, this is a finite part...
We propose a new set of rotationally and translationally invariant features for image or pattern recognition and classification. The new features are cubic polynomials in the pix...