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January 2nd, 2019, 09:46 AM  #1 
Newbie Joined: Dec 2018 From: Earth Posts: 4 Thanks: 1  Upper bound on smallest field norm divisible by p
Let $K$ be a number field, $p$ a prime ideal, $N(p)$ the norm of $p$, $P$ a principal ideal and $N(P)$ the norm of $P$. What are the (reasonable) upper bounds for the smallest $N(P)$ such that $N(p)  $N(P)$? Thanks for help. 

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