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math.NT2019★ 2 cited
On primes represented by quartic polynomials on average
Kam Hung Yau
We obtain an upper bound for the distribution of primes in the form up to , averaged over with small square-full part. As a corollary, we show that for almost all…
math.NT2019
On products of primes and square-free integers in arithmetic progressions
Kam Hung Yau
We obtain an asymptotic formula for the number of ways to represent every reduced residue class as a product of a prime and square-free integer. This may be considered as a relaxed…
math.NT2019
Representation of an integer as the sum of a prime in arithmetic progression and a square-free integer
Kam Hung Yau
Uniformly for small and , we obtain an estimate for the weighted number of ways a sufficiently large integer can be represented as the sum of a prime congruent to …