Diophantine approximation with sums of two squares II

2025/08/25 by Baier, Stephan, Rahaman, Habibur
#11E25 #11J25 #11J54 #11J71 #11L05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.18044

Abstract

Recently, we showed that for every irrational number α, there exist infinitely many positive integers n represented by any given positive definite binary quadratic form Q, satisfying ||αn||0. We also provided a quantitative version with a lower bound when the exponent 1/2-ε is replaced by weaker exponent γ<3/7-ε. In this article we recover this quantitative version with the exponent 1/2-ε, but now for the particular case of sums of two squares.

Citations

• Bounds on bilinear forms with Kloosterman sums

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