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• W4311441340 startingPage "3725" @default.
• W4311441340 abstract "Let $X$ be a quotient of the modular curve $X_0(N)$ whose Jacobian $J_X$ is a simple factor of $J_0(N)^{new}$ over $mathbb{Q}$. Let $f$ be the newform of level $N$ and weight 2 associated with $J_X$; assume $f$ has analytic rank 1. We give analytic methods for determining the rational points of $X$ using quadratic Chabauty by computing two $p$-adic Gross-Zagier formulas for $f$. Quadratic Chabauty requires a supply of rational points on the curve or its Jacobian; this new method eliminates this requirement. To achieve this, we give an algorithm to compute the special value of the anticyclotomic $p$-adic $L$-function of $f$ constructed by Bertolini, Darmon, and Prasanna, which lies outside of the range of interpolation." @default.
• W4311441340 created "2022-12-26" @default.
• W4311441340 creator A5060265443 @default.
• W4311441340 date "2023-02-28" @default.
• W4311441340 modified "2023-10-05" @default.
• W4311441340 title "Quadratic Chabauty and 𝑝-adic Gross–Zagier" @default.
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• W4311441340 doi "https://doi.org/10.1090/tran/8862" @default.
• W4311441340 hasPublicationYear "2023" @default.
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