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Arboreal Galois representation for a certain type of quadratic polynomials

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We give a description of the arboreal Galois representation of a quadratic polynomial $$f(x)=x^2-(4k+1)$$ f ( x ) = x 2 - ( 4 k + 1 ) , where… Click to show full abstract

We give a description of the arboreal Galois representation of a quadratic polynomial $$f(x)=x^2-(4k+1)$$ f ( x ) = x 2 - ( 4 k + 1 ) , where $$k\in {\mathbb {N}}$$ k ∈ N and $$4k+1$$ 4 k + 1 is not a square in $${\mathbb {Z}}$$ Z .

Keywords: certain type; type quadratic; galois representation; representation certain; arboreal galois

Journal Title: Archiv der Mathematik
Year Published: 2019

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