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Systems of cubic forms
Author(s) -
Dietmann Rainer
Publication year - 2008
Publication title -
journal of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.441
H-Index - 62
eISSN - 1469-7750
pISSN - 0024-6107
DOI - 10.1112/jlms/jdm123
Subject(s) - cubic form , dimension (graph theory) , mathematics , zero (linguistics) , pure mathematics , cubic function , space (punctuation) , mathematical analysis , computer science , philosophy , linguistics , operating system
We discuss the existence of rational and p ‐adic zeros of systems of cubic forms. In particular, we prove that for p ≠2 any system of r cubic forms over Q p in more than 125 r 3 +705 r 2 +210 r variables admits a non‐trivial p ‐adic zero, and that any system of r rational cubic forms in more than O ( r 4 m 6 + r 6 m 5 ) variables admits a rational linear space of zeros of dimension at least m .
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