Title: Constraints on counterexamples to the Casas-Alvero conjecture, and a verification in degree 12
Authors: Castryck, Wouter ×
Laterveer, Robert
Ounaïes, Myriam #
Issue Date: 2014
Publisher: American Mathematical Society
Series Title: Mathematics of Computation vol:83 issue:290 pages:3017-3037
Abstract: In the first (theoretical) part of this paper, we prove a number of constraints on hypothetical counterexamples to the Casas-Alvero conjecture, building on ideas of Graf von Bothmer, Labs, Schicho and van de Woestijne that were recently reinterpreted by Draisma and de Jong in terms of p-adic valuations. In the second (computational) part, we present ideas improving upon Diaz-Toca and Gonzalez-Vega's Gr\"obner basis approach to the Casas-Alvero conjecture. One application is an extension of the proof of Graf von Bothmer et al. to the cases 5p^k, 6p^k and 7p^k (that is, for each of these cases, we determine the finite list of primes p to which their proof is not applicable). Finally, by combining both parts, we settle the Casas-Alvero conjecture in degree 12 (the smallest open case).
ISSN: 0025-5718
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Algebra Section
× corresponding author
# (joint) last author

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casascomb.pdfMain article Accepted 225KbAdobe PDFView/Open
CAbadprimes.mmagma file Accepted 6KbView/Open
CAdeg12.mmagma file Accepted 8KbView/Open
precompscenarios12.zipmagma file Accepted 1556KbView/Open
CAbadprimes7test.mmagma file Accepted 10KbView/Open
badprimes7.txtbad primes for n=7 Accepted 6KbTextView/Open


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