论文标题
相对的菌泽尔假设
The relative Schinzel hypothesis
论文作者
论文摘要
schinzel假设是一个关于整数上一个变量不可约多项式的猜想：在某种标准条件下，它们应在整数上无限地假设许多质量值。我们考虑一个相对版本：如果多项式是相对素数，而没有质数将其所有值划分为整数，则它们在至少一个整数下假设相对质量值。我们将问题扩展到所有积分域，并证明许多问题：PID，含有无限场的UFD，在UFD上进行多项式环。应用程序包括希尔伯特不可约性定理的新“积分”版本，为此，不可约性结论在环上。
The Schinzel Hypothesis is a conjecture about irreducible polynomials in one variable over the integers: under some standard condition, they should assume infinitely many prime values at integers. We consider a relative version: if the polynomials are relatively prime and no prime number divides all their values at integers, then they assume relatively prime values at at least one integer. We extend the question to all integral domains and prove it for a number of them: PIDs, UFDs containing an infinite field, polynomial rings over a UFD. Applications include a new "integral" version of the Hilbert Irreducibility Theorem, for which the irreducibility conclusion is over the ring.
