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- W3217422597 abstract "Let $n$ be a positive square-free integer, where every odd prime factor of $n$ has form $8apm 1$. We determine when $n$ is non-congruent with second minimal $2$-primary Shafarevich-Tate group, in terms of the $4$-ranks of class groups and a Jacobi symbol. In particular, when every odd prime factor of $n$ has form $8a+1$, this condition is equivalent to the vanishing of the $4$-rank of the tame kernel of $mathbb Q(sqrt{n})$ for odd $n$, or $mathbb Q(sqrt{-n})$ for even $n$. This generalizes previous results." @default.
- W3217422597 created "2021-12-06" @default.
- W3217422597 creator A5040270192 @default.
- W3217422597 date "2021-11-22" @default.
- W3217422597 modified "2023-09-23" @default.
- W3217422597 title "On non-congruent numbers with $8apm1$ type odd prime factors and tame kernels" @default.
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- W3217422597 doi "https://doi.org/10.48550/arxiv.2111.11618" @default.
- W3217422597 hasPublicationYear "2021" @default.
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