Galois groups of some iterated polynomials over cyclotomic extensions
Sign Up to like & getrecommendations! Published in 2017 at "Archiv der Mathematik"
DOI: 10.1007/s00013-017-1120-6
Abstract: Let $$\varphi _p(z)=(z-1)^p+2-\zeta _p$$φp(z)=(z-1)p+2-ζp, where $$\zeta _p\in \bar{\mathbb {Q}}$$ζp∈Q¯ is a primitive pth root of unity. Building on previous work, we show that the nth iterate $$\varphi _p^n(z)$$φpn(z) has Galois group $$[C_p]^n$$[Cp]n, an iterated wreath… read more here.
Keywords: polynomials cyclotomic; galois groups; cyclotomic extensions; iterated polynomials ... See more keywords
Numerical Computation of Galois Groups
Sign Up to like & getrecommendations! Published in 2018 at "Foundations of Computational Mathematics"
DOI: 10.1007/s10208-017-9356-x
Abstract: The Galois/monodromy group of a family of geometric problems or equations is a subtle invariant that encodes the structure of the solutions. We give numerical methods to compute the Galois group and study it when… read more here.
Keywords: numerical computation; galois; group; galois groups ... See more keywords
Galois groups for integrable and projectively integrable linear difference equations
Sign Up to like & getrecommendations! Published in 2017 at "Journal of Algebra"
DOI: 10.1016/j.jalgebra.2017.02.032
Abstract: We consider first-order linear difference systems over C(x)C(x), with respect to a difference operator σ that is either a shift σ:x↦x+1σ:x↦x+1, q -dilation σ:x↦qxσ:x↦qx with q∈C×q∈C× not a root of unity, or Mahler operator σ:x↦xqσ:x↦xq… read more here.
Keywords: groups integrable; difference; integrable projectively; galois groups ... See more keywords
WILD RAMIFICATION IN TRINOMIAL EXTENSIONS AND GALOIS GROUPS
Sign Up to like & getrecommendations! Published in 2020 at "Glasgow Mathematical Journal"
DOI: 10.1017/s001708952000004x
Abstract: Abstract It is proven that, for a wide range of integers s (2 < s < p − 2), the existence of a single wildly ramified odd prime l ≠ p leads to either the… read more here.
Keywords: wild ramification; trinomial extensions; galois groups; ramification trinomial ... See more keywords
Infinite families of monogenic trinomials and their Galois groups
Sign Up to like & getrecommendations! Published in 2018 at "International Journal of Mathematics"
DOI: 10.1142/s0129167x18500398
Abstract: Let n ∈ ℤ with n ≥ 3. Let Sn and An denote, respectively, the symmetric group and alternating group on n letters. Let m be an indeterminate, and define fm(x) := xn + a(m,n)x… read more here.
Keywords: infinite families; families monogenic; galois groups; trinomials galois ... See more keywords