8 citations · 12 across the 4 of their papers we have counts for
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Finitely ramified iterated extensions
Wayne Aitken, Farshid Hajir, Christian Maire
Let K be a number field, t a parameter, F=K(t) and f in K[x] a polynomial of degree d. The polynomial P_n(x,t)= f^n(x) - t in F[x] where f^n is the n-fold iterate of f, is absolute…
On the Galois group of Generalized Laguerre Polynomials
Farshid Hajir
Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be ``large.'' For a fixed $α\in \Q - \Z_{<0}$, Filaseta and Lam have sh…
Algebraic properties of a family of Generalized Laguerre Polynomials
Farshid Hajir
We study the algebraic properties of Generalized Laguerre Polynomials for negative integral values of the parameter. For integers , we conjecture that $L_n^{(-1-n-r)}(x)…
Specializations of one-parameter families of polynomials
Farshid Hajir, Siman Wong
Let K be a number field, and let lambda(x,t)\in K[x, t] be irreducible over K(t). Using algebraic geometry and group theory, we study the set of alpha\in K for which the specialize…
Extensions of number fields with wild ramification of bounded depth
Farshid Hajir, Christian Maire
We consider p-extensions of number fields such that the filtration of the Galois group by higher ramification groups is of prescribed finite length. We extend well-known properties…