Matches in SemOpenAlex for { <https://semopenalex.org/work/W4226090843> ?p ?o ?g. }
Showing items 1 to 57 of
57
with 100 items per page.
- W4226090843 abstract "The Hilbert class polynomial $H_{mathcal{O}}(x)in mathbb{Z}[x]$ attached to an order $mathcal{O}$ in an imaginary quadratic field $K$ is the monic polynomial whose roots are precisely the distinct $j$-invariants of elliptic curves over $mathbb{C}$ with complex multiplication by $mathcal{O}$. Let $p$ be a prime inert in $K$ and strictly greater than $|operatorname{disc}(mathcal{O})|$. We show that the number of $mathbb{F}_p$-roots of $H_mathcal{O}(x)!! pmod{p}$ is either zero or $|operatorname{Pic}(mathcal{O})[2]|$ by exhibiting a free and transitive action of $operatorname{Pic}(mathcal{O})[2]$ on the set of $mathbb{F}_p$-roots of $H_mathcal{O}(x)!! pmod p$ whenever it is nonempty. We also provide a concrete criterion for the nonemptiness of the set of $mathbb{F}_p$-roots. A similar result was first obtained by Xiao et al.~[Int. J. Number Theory, DOI: 10.1142/S1793042122500555] and generalized much further by Li et al.~[arXiv:2108.00168] (that covers the current result) with a different approach." @default.
- W4226090843 created "2022-05-05" @default.
- W4226090843 creator A5011654282 @default.
- W4226090843 creator A5070973555 @default.
- W4226090843 date "2022-02-09" @default.
- W4226090843 modified "2023-10-18" @default.
- W4226090843 title "On $mathbb{F}_p$-roots of the Hilbert class polynomial modulo $p$" @default.
- W4226090843 doi "https://doi.org/10.48550/arxiv.2202.04317" @default.
- W4226090843 hasPublicationYear "2022" @default.
- W4226090843 type Work @default.
- W4226090843 citedByCount "0" @default.
- W4226090843 crossrefType "posted-content" @default.
- W4226090843 hasAuthorship W4226090843A5011654282 @default.
- W4226090843 hasAuthorship W4226090843A5070973555 @default.
- W4226090843 hasBestOaLocation W42260908431 @default.
- W4226090843 hasConcept C10138342 @default.
- W4226090843 hasConcept C114614502 @default.
- W4226090843 hasConcept C121332964 @default.
- W4226090843 hasConcept C134306372 @default.
- W4226090843 hasConcept C138885662 @default.
- W4226090843 hasConcept C162324750 @default.
- W4226090843 hasConcept C163635466 @default.
- W4226090843 hasConcept C182306322 @default.
- W4226090843 hasConcept C2780813799 @default.
- W4226090843 hasConcept C33923547 @default.
- W4226090843 hasConcept C41895202 @default.
- W4226090843 hasConcept C54732982 @default.
- W4226090843 hasConcept C90119067 @default.
- W4226090843 hasConceptScore W4226090843C10138342 @default.
- W4226090843 hasConceptScore W4226090843C114614502 @default.
- W4226090843 hasConceptScore W4226090843C121332964 @default.
- W4226090843 hasConceptScore W4226090843C134306372 @default.
- W4226090843 hasConceptScore W4226090843C138885662 @default.
- W4226090843 hasConceptScore W4226090843C162324750 @default.
- W4226090843 hasConceptScore W4226090843C163635466 @default.
- W4226090843 hasConceptScore W4226090843C182306322 @default.
- W4226090843 hasConceptScore W4226090843C2780813799 @default.
- W4226090843 hasConceptScore W4226090843C33923547 @default.
- W4226090843 hasConceptScore W4226090843C41895202 @default.
- W4226090843 hasConceptScore W4226090843C54732982 @default.
- W4226090843 hasConceptScore W4226090843C90119067 @default.
- W4226090843 hasLocation W42260908431 @default.
- W4226090843 hasOpenAccess W4226090843 @default.
- W4226090843 hasPrimaryLocation W42260908431 @default.
- W4226090843 hasRelatedWork W1975562561 @default.
- W4226090843 hasRelatedWork W2001958070 @default.
- W4226090843 hasRelatedWork W2049824936 @default.
- W4226090843 hasRelatedWork W2080745188 @default.
- W4226090843 hasRelatedWork W2085457124 @default.
- W4226090843 hasRelatedWork W2327819220 @default.
- W4226090843 hasRelatedWork W2562957045 @default.
- W4226090843 hasRelatedWork W2888400090 @default.
- W4226090843 hasRelatedWork W2977879719 @default.
- W4226090843 hasRelatedWork W1970258208 @default.
- W4226090843 isParatext "false" @default.
- W4226090843 isRetracted "false" @default.
- W4226090843 workType "article" @default.