3
$\begingroup$

Let $P(x)$ be a polynomial with integer coefficients, and let $p$ be a prime number. Recently, a user of MO proved that the limit $$\delta_p(P) := \lim_{n \to \infty} \frac{|\{P(x) \bmod p^n : x = 1,\dots,p^n\}|}{p^n} $$ exists and is equal to a rational number.

Is there a reference to this result in the literature?

Thanks.

Improve this question
$\endgroup$
1
  • $\begingroup$ Judging by the amount of attention attracted by that MO question (and the related math.SE one), I think we can be pretty sure that nobody on this forum knows such a reference, or they would have posted it there! Let's hope that the answer posted there gets transformed into a research article soon -- then that can become an answer to this question as well. $\endgroup$
    – David Loeffler
    Commented Oct 13, 2021 at 10:26

0

Reset to default

You must log in to answer this question.