Abstract
Suppose that λ1, λ2, λ3, λ4 are nonzero real numbers, not all negative, δ > 0, V is a well-spaced set, and the ratio λ1/λ2 is algebraic and irrational. Denote by E(V,N, δ) the number of v ∈ V with v ≤ N such that the inequality
has no solution in primes p1, p2, p3, p4. We show that
for any ɛ > 0.
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The research has been supported by the National Natural Science Foundation of China (Grants No. 11371122, 11471112), and the Research Foundation of North China University of Water Resources and Electric Power (No. 201084).
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Ge, W., Zhao, F. The exceptional set for Diophantine inequality with unlike powers of prime variables. Czech Math J 68, 149–168 (2018). https://doi.org/10.21136/CMJ.2018.0388-16
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DOI: https://doi.org/10.21136/CMJ.2018.0388-16