Powers and Polynomials in ${\Bbb Z}_m$

GLn(Fq) in polynomials modulo Frobenius powers

An improved bound on correlation between polynomials over Z_m and MOD_q

Let m, q > 1 be two integers that are co-prime and A be any subset of Zm. Let P be any multi-variate polynomial of degree d in n variables over Zm. We show that the MODq boolean function on n variables has correlation at most exp(−Ω(n/(m2 ))) with the boolean function f defined by f(x) = 1 iff P (x) ∈ A for all x ∈ {0, 1}. This improves on the bound of exp(−Ω(n/(m2))) obtained in the breakthrou...

Roots of Polynomials Modulo Prime Powers

To say that R is a root set modulo n means that R is a subset of Z n , the ring of integers modulo n , and there is a polynomial the roots of which modulo n are exactly the elements of R . Note that [ and Z n are always root sets modulo n . It seems that only two papers have appeared which mention the nature of root sets modulo n , and then only at a very basic level : Sierpin ́ ski [3] and Choj...

Patterns of Dependence Among Powers of Polynomials

Invariants of GLn(Fq) in polynomials modulo Frobenius powers