3 papers
math.NT2023
On a binary Diophantine inequality involving primes of a special type
Yuhui Liu
Let and be a sufficiently large real number. In this paper, it is proved that for any arbitrarily large number and for almost all real $R \in (N,2…
math.NT2023
On sums of unequal powers of primes and powers of 2
Yuhui Liu
In this paper, it is proved that every sufficiently large even integer can be represented as the sum of two squares of primes, two cubes of primes, two biquadrates of primes and 16…
math.NT2023
The exceptional set for Diophantine approximation with mixed powers of prime variables
Yuhui Liu
Let lambda_1, λ_2, λ_3, λ_4 be non-zero real numbers, not all negative, with λ_1/λ_2 irrational and algebraic. Suppose that \mathcal{V} is a well-spaced sequence and δ>0. In this p…