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- W2895898573 abstract "Let $K$ be an imaginary quadratic field of discriminant $d_K$, and let $mathfrak{n}$ be a nontrivial integral ideal of $K$ in which $N$ is the smallest positive integer. Let $mathcal{Q}_N(d_K)$ be the set of primitive positive definite binary quadratic forms of discriminant $d_K$ whose leading coefficients are relatively prime to $N$. We adopt an equivalence relation $sim_mathfrak{n}$ on $mathcal{Q}_N(d_K)$ so that the set of equivalence classes $mathcal{Q}_N(d_K)/sim_mathfrak{n}$ can be regarded as a group isomorphic to the ray class group of $K$ modulo $mathfrak{n}$. We further present an explicit isomorphism of $mathcal{Q}_N(d_K)/sim_mathfrak{n}$ onto $mathrm{Gal}(K_mathfrak{n}/K)$ in terms of Fricke invariants, where $K_mathfrak{n}$ is the ray class field of $K$ modulo $mathfrak{n}$. This would be a certain extension of the classical composition theory of binary quadratic forms, originated and developed by Gauss and Dirichlet." @default.
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- W2895898573 date "2018-10-15" @default.
- W2895898573 modified "2023-09-27" @default.
- W2895898573 title "On some extension of Gauss' work and applications" @default.
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