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• W3100282956 startingPage "1395" @default.
• W3100282956 abstract "Let $K$ be a totally real field. By the asymptotic Fermat's Last Theorem over $K$ we mean the statement that there is a constant $B_K$ such that for prime exponents $p>B_K$ the only solutions to the Fermat equation $a^p + b^p + c^p = 0$ with $a$, $b$, $c$ in $K$ are the trivial ones satisfying $abc = 0$. With the help of modularity, level lowering and image of inertia comparisons we give an algorithmically testable criterion which if satisfied by $K$ implies the asymptotic Fermat's Last Theorem over $K$. Using techniques from analytic number theory, we show that our criterion is satisfied by $K = mathbb{Q}(sqrt{d})$ for a subset of $d$ having density $5/6$ among the squarefree positive integers. We can improve this to density 1 if we assume a standard Eichler-Shimura conjecture." @default.
• W3100282956 created "2020-11-23" @default.
• W3100282956 creator A5012345793 @default.
• W3100282956 creator A5017561176 @default.
• W3100282956 date "2015-03-06" @default.
• W3100282956 modified "2023-10-18" @default.
• W3100282956 title "The asymptotic Fermat’s Last Theorem for five-sixths of real quadratic fields" @default.
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• W3100282956 doi "https://doi.org/10.1112/s0010437x14007957" @default.
• W3100282956 hasPublicationYear "2015" @default.
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