标题： 满足增长约束的整数值多项式 显示英文标题

标题： Integer-valued polynomials satisfying growth constraints

摘要： 我们考虑在整数上取整数值的多项式（IVPs），并且满足自然数上的额外增长条件。Elkies和Speyer回答了Dimitrov的问题，表明存在一个临界指数增长阈值，使得有无限多个IVPs的增长高于该阈值，而低于该阈值的IVPs是有限的（可以是任意次数的）。在本文中，我们给出了关于具有指数增长阈值的IVPs数量的更精细估计。此外，我们考虑了一个类似的问题，其中在整数上有（不一定对称）的增长条件。值得注意的是，临界阈值由一个显式区域的对数容量决定。 显示英文摘要

摘要： We consider polynomials which take integer values on the integers (IVPs), and satisfy an additional growth condition on the natural numbers. Elkies and Speyer, answering a question by Dimitrov, showed there is a critical exponential growth threshold, such that there are infinitely many IVPs with growth above the threshold and finitely many IVPs below that threshold (of arbitrary degree). In this paper, we give more refined estimates for the number of IVPs having exponential growth thresholds. In addition, we consider a similar problem, where there is a (not necessarily symmetric) growth condition on the integers. Notably, the critical threshold is determined by the logarithmic capacity of an explicit domain.