Taking cube roots in Zm

Formulas for cube roots in F3m

We determine the number of nonzero coefficients (called the Hamming weight) in the polynomial representation of x in F3m = F3[x]/(f), where f ∈ F3[x] is an irreducible trinomial.

Roots of cube polynomials of median graphs

Note on Taking Square-Roots Modulo

In this contribution it is shown how Gauss’ famous cyclotomic sum formula can be used for extracting square-roots modulo .

MULTIPLICATIVE GROUPS IN Zm

Our goal will be to find subsets of Zm that form groups under the operation of multiplication modulo m. By utilizing the isomorphism Zm ∼= Zn ⊕ Zk, we will find multiplicative groups contained in Zn ⊕ Zk and then map these back to Zm. In particular, if m = nk with gcd(n, k) = 1, our objective is to find particular multiplicative subsets of Zn × Zk that are groups and whose first coordinate is a...

DIAGONAL COINVARIANTS OF Zm ≀ Sn

We construct a quotient ring of the ring of diagonal coinvariants of the complex reflection group W = G(m, 1, n) and determine its graded character. This generalises a result of Gordon for Coxeter groups. The proof uses a study of category O for the rational Cherednik algebra of W , including a shift isomorphism which is proved in Appendix 1.