HAL will be down for maintenance from Friday, June 10 at 4pm through Monday, June 13 at 9am. More information
Skip to Main content Skip to Navigation
Preprints, Working Papers, ...

Schertz style class invariants for quartic CM fields

Andreas Enge 1 Marco Streng 2
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, ...
Complete list of metadata

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
Files produced by the author(s)

Identifiers

  • HAL Id : hal-01377376, version 2

Collections

Citation

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

Share

Metrics

Record views

370

Files downloads

131