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- W879823654 abstract "Let K denote a p-adic field and $F_1,..,F_r in k[x_1, . . . , x_n]$ be forms with respective degrees $d_1, . . . , d_r$. A contemporary version of a conjecture attributed to E. Artin states that $F_1, . . . , F_r$ have a common non-trivial zero whenever $n > d_1^2 + · · · + d_r^2$.We prove this for a single quintic form $(i.e.~ r = 1, d_1 = 5)$, providedthat the cardinality of the residue class field exceeds 9. We also verifythe conjecture for a system comprising a cubic and a quadratic form$(i.e.~r = 2, d_1 = 3, d_2 = 2)$, whenever the residue class field is ofcharacteristic at least 13 and has more than 37 elements." @default.
- W879823654 created "2016-06-24" @default.
- W879823654 creator A5077794716 @default.
- W879823654 date "2014-11-06" @default.
- W879823654 modified "2023-09-27" @default.
- W879823654 title "Diophantine Equations in Many Variables" @default.
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- W879823654 hasPublicationYear "2014" @default.
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