English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we extend our recent results concerning the validity of the law of inertia for the factorization of cubic polynomials over the Galois fieldF   p    $\Bbb F_p$   ,  p  being a prime. As the main result, the following theorem will be proved: LetD  ∈   Z    $D\in \Bbb Z$    and let  C D   be the set of all cubic polynomialsx  3   +  a   x  2   +  b  x  +  c  ∈   Z   [  x  ]   $x^3+ax^2+bx+c\in\Bbb Z[x]$    with a discriminant equal to  D . If  D  is square-free and3  ∤  h  (  −  3  D  )   $3\nmid h(-3D)$    whereh  (  −  3  D  )   $h(-3D)$    is the class number ofQ   (   −  3  D   )   $\Bbb Q(\sqrt {-3D})$   , then all cubic polynomials in  C D   have the same type of factorization over any Galois fieldF   p    $\Bbb F_p$    where  p  is a prime,  p  &gt; 3.

Law of inertia for the factorization of cubic polynomials — the case of discriminants divisible by three