On the exponent of the ideal class group of 𝑄(√-𝑑)

Pappalardi, Francesco

doi:10.1090/S0002-9939-1995-1233979-7

On the exponent of the ideal class group of $\textbf {Q}(\sqrt {-d})$
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by Francesco Pappalardi

Proc. Amer. Math. Soc. 123 (1995), 663-671

DOI: https://doi.org/10.1090/S0002-9939-1995-1233979-7

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Abstract:

Let $m(d)$ be the exponent of the ideal class group of ${\mathbf {Q}}(\sqrt { - d} )$, we establish the bound $m(d) \gg \frac {{\log d}}{{\log \log d}}$ for almost all the discriminants d by using uniform asymptotic formulas on the number of $n \leq x$ for which there exists a prime less than s for which n is a quadratic residue.

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