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# Schertz style class invariants for quartic CM fields

1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : A class invariant is a CM value of a modular function that lies in a certain unram-ified class field. We show that Siegel modular functions over $Q$ for $Γ^0 (N) ⊆ Sp_4 (Z)$yield class invariants under some splitting conditions on N. Small class invariants speed up constructions in explicit class field theory and public-key cryptography. Our results generalise results of Schertz's from elliptic curves to abelian varieties and from classical modular functions to Siegel modular functions.
Document type :
Preprints, Working Papers, ...

https://hal.inria.fr/hal-01377376
Contributor : Andreas Enge Connect in order to contact the contributor
Submitted on : Friday, May 28, 2021 - 4:52:33 PM
Last modification on : Wednesday, February 2, 2022 - 3:53:55 PM

### Files

classinv.pdf
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### Identifiers

• HAL Id : hal-01377376, version 2

### Citation

Andreas Enge, Marco Streng. Schertz style class invariants for quartic CM fields. 2016. ⟨hal-01377376v2⟩

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