A Diophantine approximation problem with two primes and one k-th power of a prime

2017/05/31 by Alessandro Gambini, Alessandro Languasco, Gambini, Alessandro +3 · 2 citations
#Analytic Number Theory Research #Algebraic Geometry and Number Theory #Mathematical Dynamics and Fractals

paper · pdf · doi:10.1016/j.jnt.2018.01.002

Abstract

We refine a result of the last two Authors of [8] on a Diophantine approximation problem with two primes and a k-th power of a prime which was only proved to hold for 1<k<4/3. We improve the k-range to 1<k≤ 3 by combining Harman's technique on the minor arc with a suitable estimate for the L⁴-norm of the relevant exponential sum over primes S_k. In the common range we also give a stronger bound for the approximation.

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