13 research outputs found
Mehr Strukturwandel für Wachstum und Beschäftigung : die deutsche Wirtschaft im Anpassungsstau.
Get PDFStandortfaktor; Strukturpolitik; Deutschland;
Über die Darstellung der ganzen Spitzenformen zu den Idealstufen der Hilbertschen Modulgruppe und die Abschätzung ihrer Fourierkoeffizienten
No full textMehr Strukturwandel für Wachstum und Beschäftigung: die deutsche Wirtschaft im Anpassungsstau
Full text linkIdentification of High Potency Microbial and Self Ligands for a Human Autoreactive Class II–restricted T Cell Clone
No full textIsogenies for Point Counting on Genus Two Hyperelliptic Curves with Maximal Real Multiplication
No full textInternational audienceSchoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations of modular polynomials, and by Elkies, using a theory of explicit isogenies. Moving to Jacobians of genus-2 curves, the current state of the art for point counting is a generalization of Schoof's algorithm. While we are currently missing the tools we need to generalize Elkies' methods to genus 2, recently Martindale and Milio have computed analogues of modular polynomials for genus-2 curves whose Jacobians have real multiplication by maximal orders of small discriminant. In this article, we prove Atkin-style results for genus-2 Jacobians with real multiplication by maximal orders, with a view to using these new modular polynomials to improve the practicality of point-counting algorithms for these curves
