整系数多项式光滑值数量的一个上界及其应用
An upper bound for the number of smooth values of a polynomial and its applications
AI总结：
本文证明了整系数多项式光滑值数量的新上界，改进了Timofeev的结果，并应用于Cassels定理的另证及二次多项式本原因子问题。
摘要：
我们证明了整系数多项式光滑值数量的一个新上界。除非该多项式是整系数线性多项式的乘积，否则这一结果改进了Timofeev的先前结果。作为应用，我们为Cassels的一个结果提供了另一种证明，该结果曾被用于证明具有代数无理参数的Hurwitz zeta函数在收敛域上有无穷多个零点。我们还将主要结果应用于二次多项式本原因子的问题。
英文摘要：
We prove a new upper bound for the number of smooth values of a polynomial with integer coefficients. This improves Timofeev's previous result unless the polynomial is a product of linear polynomials with integer coefficients. As an application, we provide another proof for a result of Cassels which was used to prove that the Hurwitz zeta-function with algebraic irrational parameter has infinitely many zeros on the domain of convergence. We also apply the main result to a problem on primitive divisors of quadratic polynomials.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
