C. Lau

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20242026

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math.NT2024

Residue Class Patterns of Consecutive Primes

Cheuk Fung Lau

Dickson's conjecture and the Hardy--Littlewood prime tuple conjecture predict that every pattern of reduced residue classes modulo $q$ is attained by infinitely many strings of $m$ …

math.NT2024

Simultaneously Small Fractional Parts of Polynomials

Cheuk Fung Lau

Let $f_{1}, \dots, f_{k} \in R [X]$ be polynomials of degree at most $d$ with $f_{1} (0) = \dots = f_{k} (0) = 0$ . We show that there is an $n < x$ such that $\|f_i(n)\|\ll x^{-1/10.5kd(d-1)+o…