论文标题
在伪级别上，仅由一组稀疏的素数和$ \ a $ pseudo-Pseudo-polynomials排除
On pseudo-polynomials divisible only by a sparse set of primes and $\a$-primary pseudo-polynomials
论文作者
论文摘要
我们探索了有关伪polynomials的两个问题，它们是函数$ f：\ mathbb n \ to \ mathbb z $，以至于$ k $ divides $ f（n+k） - f（n+k） - f（n）$ for All $ n，k $。首先，对于某些任意稀疏集$ r $，我们构建了pseudo-polynomials $ f $，$ p | f（n）$ for Bosy $ n $仅在r $中的$ n $时。这意味着，并非所有伪多项式都满足了Kowalski和Soundararajan的最新论文的假设。我们还考虑了$α$ - 主要的伪型聚合物，其中仅在一组primes primes $α$的psseudo-polynomial条件下才需要伪单位条件。我们表明，如果$α$ - 主要的伪polynomial为$ o（e^{（2/3-ε）n}）$，那么它是多项式。
We explore two questions about pseudo-polynomials, which are functions $f:\mathbb N \to \mathbb Z$ such that $k$ divides $f(n+k) - f(n)$ for all $n,k$. First, for certain arbitrarily sparse sets $R$, we construct pseudo-polynomials $f$ with $p|f(n)$ for some $n$ only if $p \in R$. This implies that not all pseudo-polynomials satisfy an assumption of a recent paper of Kowalski and Soundararajan. We also consider $α$-primary pseudo-polynomials, where the pseudo-polynomial condition is only required for $k$ lying in a set of primes of density $α$. We show that if an $α$-primary pseudo-polynomial is $O(e^{(2/3-ε) n})$, then it is a polynomial.
