AN ALGORITHM FOR COMPUTING THE STICKELBERGER IDEAL FOR MULTIQUADRATIC NUMBER FIELDS

Autor:	D. O. Olefirenko, E. A. Kirshanova, E. S. Malygina, S. A. Novoselov
Rok vydání:	2021
Předmět:	Ideal (set theory) Computational Theory and Mathematics Applied Mathematics Signal Processing Discrete Mathematics and Combinatorics Applied mathematics Algebraic number field Theoretical Computer Science Mathematics
Zdroj:	Prikladnaya Diskretnaya Matematika. :9-30
ISSN:	2311-2263 2071-0410
Popis:	We present an algorithm for computing the Stickelberger ideal for multiquadratic fields K = Q(√d1,√d2, . . . , √dn), where the integers di ≡ 1 mod 4 for i ∈ {1, . . . , n} or dj ≡ 2 mod 8 for one j ∈ {1, . . . , n}; all di’s are pairwise co-prime and squarefree. Our result is based on the paper of Kuˇcera [J. Number Theory, no. 56, 1996]. The algorithm we present works in time O(lg ∆K • 2n• poly(n)), where ∆K is the discriminant of K. As an interesting application, we show a connection between Stickelberger ideal and the class number of a multiquadratic field
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::a19d8ed5e3ec0b8e63bf77fdf7d78041 https://doi.org/10.17223/20710410/51/1 Zobrazit plný text záznamu