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An application of the $p$ -adic analytic class number formula

  • Claus Fieker (a1) and Yinan Zhang (a2)

Abstract

We propose an algorithm to verify the $p$ -part of the class number for a number field $K$ , provided $K$ is totally real and an abelian extension of the rational field $\mathbb{Q}$ , and $p$ is any prime. On fields of degree 4 or higher, this algorithm has been shown heuristically to be faster than classical algorithms that compute the entire class number, with improvement increasing with larger field degrees.

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References

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An application of the $p$ -adic analytic class number formula

  • Claus Fieker (a1) and Yinan Zhang (a2)

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