Year: 2024
Type: preprint
Abstract: We develop a sieve that can detect primes in multiplicatively structured sets under certain conditions. We apply it to obtain a new $L$-function free proof of Linnik's problem of bounding the least prime $p$ such that $p\equiv a\pmod q$ (with the bound $p \ll q^{350}$) as well as a new $L$-function free proof that the interval $(x-x^{39/40}, x]$ contains primes for every large $x$. In a future work we will develop the sieve further and provide more applications.
Source: arXiv (Cornell University)
Institution: University of Turku
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: Research in Mathematics, G434337789
OpenAlex ID: W4391462640