4 papers
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…
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…
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 …
Smooth squarefree and square-full integers in arithmetic progressions
Marc Munsch, Igor E. Shparlinski, Kam Hung Yau
We obtain new lower bounds on the number of smooth squarefree integers up to in residue classes modulo a prime , relatively large compared to , which in some ranges of $p…