𝑝-adic computation of real quadratic class numbers

Buchmann, J.; Sands, J. W.; Williams, H. C.

doi:10.1090/S0025-5718-1990-1010596-9

$p$-adic computation of real quadratic class numbers
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by J. Buchmann, J. W. Sands and H. C. Williams PDF

Math. Comp. 54 (1990), 855-868 Request permission

Abstract:

Let $\mathcal {K}$ be any real quadratic field and let ${h_\mathcal {K}}$ be the class number of $\mathcal {K}$. A method utilizing the p-adic class number formula for $\mathcal {K}$ is described for evaluating ${h_\mathcal {K}}$. The technique was programmed for a micro VAX II computer and run on all fields $\mathcal {K}$ with radicand $< {10^6}$.

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