论文标题
存在有限磁场上有规定痕迹的原始对的存在
Existence of Primitive Pairs with Prescribed Traces over Finite Fields
论文作者
论文摘要
令$ f = \ mathbb {f} _ {q^m} $，$ m> 6 $，$ n $ a正整数和$ f = p/q $，$ p $，$ q $ c $ co $ co co co prime norrime dromibils in $ f [x] $和deg $ $ f [x] $和deg $ $ $ $ $+$+$+$+$+$（q）= n $。对于$ f $中的原始对$（α，f（α））$的存在已经获得了足够的条件，以至于对于任何规定的$ a，b $ in $ e = \ mathbb {f} _q $，tr $ f/e（α）= a $和tr $ f/e（a $ f/e）此外，对于每个正整数$ n $，肯定存在足够大的$（q，m）$的一对。 CASE $ n = 2 $是单独交易的，并证明了所有$（Q，m）$除了最多64美元的选择。
Let $F=\mathbb{F}_{q^m}$, $m>6$, $n$ a positive integer, and $f=p/q$ with $p$, $q$ co-prime irreducible polynomials in $F[x]$ and deg$(p)$ $+$ deg$(q)= n$. A sufficient condition has been obtained for the existence of primitive pairs $(α, f(α))$ in $F$ such that for any prescribed $a, b$ in $E=\mathbb{F}_q$, Tr$F/E (α) = a$ and Tr$F/E (α^{-1}) = b$. Further, for every positive integer $n$, such a pair definitely exists for large enough $(q,m)$. The case $n = 2$ is dealt separately and proved that such a pair exists for all $(q,m)$ apart from at most $64$ choices.
