指数对理论

The Theory of Exponent Pairs

1 指数对的定义和基本性质 定义 设f:(N,2N]→R满足:f(x)有无穷多阶导数且存在y>0,s>0,使得对所有整数q≥0及N<x≤2N。

Let F be the set of exponent pairs generated by the A and B process.For θ(λ,μ) - (aλ, + bμ + c)/(dλ + eμ + f) such that dλ+ eμ +f>0 holds for any (λ,μ)∈F, a necessary and sufficient condition for which inf θ=θ(λθ,μθ) , (λθ,μθ) ∈F was obtained, and a criterion to determine whether inf θ = inf θA or inf θ - inf θBA. This is an improvement of Graham's results. Finally, a conjecture on the complete determination is proposed.