Algebraic properties of Kaneko-Zagier lifts of supersingular polynomials

Algebraic properties of Kaneko-Zagier lifts of supersingular polynomials

studied lifts to \mathbf {Q}[x]. Among these is one introduced by Kaneko and Zagier, which, when interpreted as a specialized Jacobi polynomial, is seen to coincide with a lift discovered by Brillhart and Morton a few years later. The algebraic properties of this family of lifts of \mathfrak{S}_\ell...

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Veröffentlicht in:Proceedings of the American Mathematical Society 2017-06, Vol.145 (6), p.2291-2304
Hauptverfasser: CULLINAN, JOHN, HAJIR, FARSHID
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A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
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description studied lifts to \mathbf {Q}[x]. Among these is one introduced by Kaneko and Zagier, which, when interpreted as a specialized Jacobi polynomial, is seen to coincide with a lift discovered by Brillhart and Morton a few years later. The algebraic properties of this family of lifts of \mathfrak{S}_\ell (x) are not well-understood. We focus on a conjecture of Mahlburg and Ono regarding the maximality of their Galois groups (when shorn of their trivial linear factors) and also establish their irreducibility in some previously unknown cases.]]>
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subjects A. ALGEBRA, NUMBER THEORY, AND COMBINATORICS
title Algebraic properties of Kaneko-Zagier lifts of supersingular polynomials
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