Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5772607 | Journal of Number Theory | 2017 | 17 Pages |
Abstract
Let λ1,â¦,λ4 be non-zero real numbers, not all of the same sign, with λ1/λ2 irrational, and Ï be a real number. We prove that for any ε>0, the inequality|λ1p1+λ2p22+λ3p32+λ4p42+Ï|â¤(maxâ¡{p1,p22,p32,p42})â114+ε has infinitely many solutions in prime variables p1,â¦,p4. If we further assume that λ1/λ3 is also irrational and λ1/λ2, λ1/λ3 are both algebraic, then we may replace the exponent by â340+ε.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory
Authors
Yuchao Wang, Weili Yao,