arXiv subjects

Valeriia Starichkova

Publications and source records attributed to Valeriia Starichkova.

4 recordsLinked to original sources

arXiv2026

The determination of norm-Euclidean cyclic cubic fields

It is known on the Generalised Riemann Hypothesis that there are precisely $13$ cyclic cubic fields that are norm-Euclidean. Unconditionally, there is a gap between analytic estimates which hold for all sufficiently large conductors and computational techniques. In this paper, we establish new results concerning explicit bounds for cubic non-residues and refine previous computational techniques, enabling us to completely characterise all norm-Euclidean cyclic cubic fields.

math.NT↗

arXiv2025

An explicit version of Chen's theorem and the linear sieve

Drawing inspiration from the work of Nathanson and Yamada we prove that every even integer larger than $\exp (\exp (32.7))$ can be written as the sum of a prime and the product of at most two primes.

math.NT↗

arXiv2024

A note on zero-density approaches for the difference between consecutive primes

In this note, we generalise two results on prime numbers in short intervals. The first result is Ingham's theorem which connects the zero-density estimates with short intervals where the prime number theorem holds, and the second result is due to Heath-Brown and Iwaniec, which derives the weighted zero-density estimates used for obtaining the lower bound for the number of primes in short intervals. The generalised versions of these results make the connections between the zero-free regions, zero-density estimates, and the primes in short intervals more transparent. As an example, the generalisation of Ingham's theorem implies that, under the Density Hypothesis, the prime number theorem holds in $[x - \sqrt{x}\exp(\log^{2/3+\varepsilon}x), x]$, which refines upon the classic interval $[x - x^{1/2+ \varepsilon}, x]$.

math.NT↗

arXiv2022

An explicit version of Chen's theorem assuming the Generalized Riemann Hypothesis

We prove that assuming the Generalized Riemann Hypothesis every even integer larger than $\exp(\exp(15.85))$ can be written as the sum of a prime number and a number that has at most two prime factors.

math.NT↗