Values of binary linear forms at prime arguments

Abstract

value of a given binary linear form at prime arguments. Let λ₁ and λ₂ be positive real numbers such that λ₁/λ₂ is irrational and algebraic. For any (C, c) well-spaced sequence {V} and δ>0, let E({V}, X, δ) denote the number of υ∈{V} with υ≤X for which the inequality

has no solution in primes p₁, p₂. It is shown that for any ε>0,we have E({V}, X, δ) «max(X^{\frac{\mathrm{3}}{\mathrm{5}}+\mathrm{2}\delta +\epsilon },X^{\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{4}}{\mathrm{3}}\delta +\epsilon }).

Keywords

Circle method / Diophantine inequality

References

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