Joachim König

On intersective polynomials with non-solvable Galois group

ABSTRACT We present new theoretical results on the existence of intersective polynomials (that is, integer polynomials with roots in all ℚp, but not in ℚ) with certain prescribed Galois groups, namely the projective and affine linear groups PGL2(ℓ) and AGL2(ℓ) as well as the affine symplectic groups . For further families of affine groups, existence results are proven conditional on the existence on certain tamely ramified Galois extensions. We also compute explicit families of intersective polynomials for certain non-solvable groups.

Computation of Hurwitz spaces and new explicit polynomials for almost simple Galois groups

We compute the first explicit polynomials with Galois groups

A note on the product of two permutations of prescribed orders

G=P\Gamma L_3(4)

Solvability of generalized monomial groups

,

Galois realizations with inertia groups of order two

PGL_3(4)

On the Local Behavior of Specializations of Function Field Extensions

,

Non-parametricity of rational translates of regular Galois extensions

PSL_3(4)

Non-parametric sets of regular realizations over number fields

and

The Grunwald problem and specialization of families of regular Galois extensions

PSL_5(2)

Septic equations are solvable by 2-fold origami

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