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- W4302011692 abstract "We study the discriminants of the minimal polynomials $mathcal{P}_n$ of the Ramanujan $t_n$ class invariants, which are defined for positive integers $nequiv11pmod{24}$. The historical precedent for doing so comes from Gross and Zagier, which is known for computing the prime factorizations of certain resultants and discriminants of the Hilbert class polynomials $H_n$. We show that $Deltaleft(mathcal{P}_nright)$ divides $Deltaleft(H_nright)$ with quotient a perfect square, and as a consequence, we explicitly determine the sign of $Deltaleft(mathcal{P}_nright)$ based on the class group structure of the order of discriminant $-n$. We also show that the discriminant of the number field generated by $jleft(frac{-1+sqrt{-n}}{2}right)$, where $j$ is the $j$-invariant, divides $Deltaleft(mathcal{P}_nright)$. Moreover, we show that 3 never divides $Deltaleft(mathcal{P}_nright)$ for all squarefree positive integers $nequiv11pmod{24}$." @default.
- W4302011692 created "2022-10-06" @default.
- W4302011692 creator A5034986876 @default.
- W4302011692 date "2022-10-02" @default.
- W4302011692 modified "2023-09-28" @default.
- W4302011692 title "On discriminants of minimal polynomials of the Ramanujan $t_n$ class invariants" @default.
- W4302011692 doi "https://doi.org/10.48550/arxiv.2210.00681" @default.
- W4302011692 hasPublicationYear "2022" @default.
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