Year: 2025
Type: preprint
Abstract: We study recurrence along shifted primes with restricted digits. By constructing a local approximant to the associated exponential sums, we prove the van der Corput property for shifted primes with restricted digits. This in turn shows that if $A\subset \mathbb{N}$ has positive upper Banach density, then there exists some prime $p$ with restricted digits and two elements $a_1,a_2\in A$ such that $a_1+p-1=a_2$.
Source: arXiv (Cornell University)
Author: Burgin, Alex
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4415274480