3 papers
math.NT2026
On Lenstra's criterion for norm-Euclideanity of number fields and properties of Dedekind zeta-functions
Jordan Pertile, Valeriia V. Starichkova
In 1977, Lenstra provided a criterion for norm-Euclideanity of number fields and noted that this criterion becomes ineffective for number fields of large enough degrees under the G…
math.NT2025
An explicit version of Chen's theorem and the linear sieve
Matteo Bordignon, Daniel R. Johnston, Valeriia Starichkova
Drawing inspiration from the work of Nathanson and Yamada we prove that every even integer larger than can be written as the sum of a prime and the product of…
math.NT2025
Some explicit results on the sum of a prime and an almost prime
Daniel R. Johnston, Valeriia V. Starichkova
Inspired by a classical result of Rényi, we prove that every even integer can be written as the sum of a prime and a number with at most 395 prime factors. We also show,…