@article{Han2025, 
author = {Xue Han and Rui Zhang},
title = {Goldbach-Linnik type problems for mixed powers of primes and powers of 2},
year = {2025},
journal = {Electronic Research Archive},
volume = {33},
number = {12},
pages = {7902-7917},
keywords = {circle method, exponential sums, Goldbach-Linnik type problem, powers of 2, primes},
url = {https://www.sciopen.com/article/10.3934/era.2025348},
doi = {10.3934/era.2025348},
abstract = {Let        p          1        ,      p          2        ,  …  ,      p          7       be primes. In this paper, we first show that when        k          1        =  23, every sufficiently large odd integer can be represented as the sum of one prime square, five prime cubes, one prime biquadrate and at most        k          1       powers of    2. We further prove that for        k          2        =  45, every pair of sufficiently large odd integers satisfying certain necessary conditions can be represented as a pair of equations involving one prime square, five prime cubes, one prime biquadrate and at most        k          2       powers of    2.}
}