Numbers with at most $2$ prime factors in short arithmetic progressions

Mayank Pandey

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arXiv · 2307.14890

Numbers with at most $2$ prime factors in short arithmetic progressions

Mayank Pandey

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Abstract

We show that if $\frac{L}{\varphi(q)\log X}\to\infty$ as $X\to\infty$, almost all $(a, x)\in (\mathbb Z/q\mathbb Z)^\times\times [X, 2X]$ are such that there exists a product of at most two primes in $[x, x + L]$ congruent to $a\mod{q}$.

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Mayank Pandey. 2023-07-27. Numbers with at most $2$ prime factors in short arithmetic progressions. https://arxiv.org/abs/2307.14890

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