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Arithmetic of Jacobi polynomials

Contributed by Khai Hoan Nguyen Dang

We study the arithmetic of Jacobi polynomials. As applications, we prove the Mahlburg--Ono conjecture on the irreducibility and Galois groups of the four Kaneko--Zagier families, and the Cullinan--Hajir conjecture on the Galois groups of Legendre polynomials. Other applications concern common zeros of Jacobi polynomials, harmonic functions on cones, and hyperelliptic Jacobians.

A mix of human-written and AI-generated textHuman understanding: some partsJacobi polynomialKaneko--Zagier polynomialLegendre polynomial

Oct 22, 2026PDF ↗View work →

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Arithmetic of Jacobi polynomials

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