38 citations · 38 across the 3 of their papers we have counts for
8 papers
Everywhere ramified towers of global function fields
Iwan Duursma, Bjorn Poonen, Michael Zieve
We consider a tower of function fields F_0 < F_1 < ... over a finite field such that every place of every F_i ramified in the tower and the sequence genus(F_i)/[F_i:F_0] has a fini…
Symplectic spreads and permutation polynomials
Simeon Ball, Michael E. Zieve
Every symplectic spread of PG(3,q), or equivalently every ovoid of Q(4,q), is shown to give rise to a certain family of permutation polynomials of GF(q) and conversely. This leads…
On Ritt's polynomial decomposition theorems
Michael E. Zieve, Peter Mueller
Ritt studied the functional decomposition of a univariate complex polynomial f into prime (indecomposable) polynomials, f = u_1 o u_2 o ... o u_r. His main achievement was a proced…
Analogues of the Jordan-Holder theorem for transitive G-sets
Greg Kuperberg, Michael Zieve
Let G be a transitive group of permutations of a finite set X, and suppose that some element of G has at most two orbits on X. We prove that any two maximal chains of groups betwee…
Decompositions of Laurent polynomials
Michael E. Zieve
In the 1920's, Ritt studied the operation of functional composition g o h(x) = g(h(x)) on complex rational functions. In the case of polynomials, he described all the ways in which…
Nonexistence of permutation binomials of certain shapes
Ariane M. Masuda, Michael E. Zieve
Suppose x^m + c*x^n is a permutation polynomial over GF(p), where p>5 is prime, m>n>0, and c is in GF(p)^*. We prove that gcd(m-n,p-1) is not 2 or 4. In the special case that eithe…