论文标题

关于Artin的猜想:一对添加形式

On Artin's Conjecture: Pairs of Additive Forms

论文作者

Kaesberg, Miriam Sophie

论文摘要

已经确定,对于每对添加表$ f = \ sum_ {i = 1}^s a_i x_i^k,g = \ sum_ {i = 1}^s b_i x_i x_i x_i x_i^k $ $ k $ in $ s> s> 2k^2 $ f = g = g = g = g = g = g = g = g = g = 0 $ p $ p $ p $ p p prime prime prime prime prime prime prime prime odd prime prime odd prime odd prime odd prime。

It is established that for every pair of additive forms $f=\sum_{i=1}^s a_i x_i^k, g=\sum_{i=1}^s b_i x_i^k$ of degree $k$ in $s>2k^2$ variables the equations $f=g=0$ have a non-trivial $p$-adic solution for all odd primes $p$.

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