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International Algorithmic Number Theory Symposium

ANTS 1994: Algorithmic Number Theory pp 234–247Cite as

Under the assumption of the Generalized Riemann Hypothesis verifying the class number belongs to NP ∩ co-NP

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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 877))

Abstract

We show that under the assumption of a certain Generalized Riemann Hypothesis the problem of verifying the value of the class number of an arbitrary algebraic number field F of arbitrary degree belongs to the complexity class NP ∩ co-NP. In order to prove this result we introduce a compact representation of algebraic integers which allows us to represent a system of fundamental units by (2 + log2(Δ))O(1) bits, where Δ is the discriminant of F.

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Authors and Affiliations

  1. Fachbereich Informatik, Universität des Saarlandes, Postfach 151150, D-66041, Saarbrücken, Germany

    Christoph Thiel

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  1. Christoph Thiel
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Leonard M. Adleman Ming-Deh Huang

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© 1994 Springer-Verlag Berlin Heidelberg

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Thiel, C. (1994). Under the assumption of the Generalized Riemann Hypothesis verifying the class number belongs to NP ∩ co-NP. In: Adleman, L.M., Huang, MD. (eds) Algorithmic Number Theory. ANTS 1994. Lecture Notes in Computer Science, vol 877. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-58691-1_61

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  • DOI: https://doi.org/10.1007/3-540-58691-1_61

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58691-3

  • Online ISBN: 978-3-540-49044-9

  • eBook Packages: Springer Book Archive

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