The authors would like to express their gratitude to the referee for his or her careful reading and valuable suggestions;This work was supported by the National Natural Science Foundation of China(Grant Nos.11771256,11971476).
Let c>1 and 0<γ<1.We study the solubility of the Diophantine inequality∣p^(c)_(1)+p^(c)_(2)+…+p^(c)_(s)−N∣<(log N)^(−1) in Piatetski-Shapiro primes p_(1),p_(2),…,p_(s) of the form pj=[m^(1/γ)]for some m∈ℕ,and i...
The authors thank the referees for their time and comments. This work was supported by the National Natural Science Foundation of China (Grant Nos. 11871193, 11471112);the Key Research Project of Henan Province Higher Education (No. 17A110009).
Let λ1,λ2,λ3,λ4 be non-zero real numbers, not all of the same sign, w real. Suppose that the ratios λ1/λ2,λ1/λ3 are irrational and algebraic. Then there are infinitely many solutions in primes pj, j = 1, 2,3,4...