Title: DIOPHANTINE APPROXIMATION WITH HARDY–LITTLEWOOD NUMBERS
Abstract: In this paper, we consider Diophantine approximation using numbers which are a sum of a prime and a square (Hardy–Littlewood Numbers). We use exponential sums and sieve methods to establish, for any irrational α and arbitrary real β, that there are infinitely many solutions to ∥ α n + β ∥ < n ε − 5 / 8 , n = p + m 2 , p a prime , where ∥ · ∥ denotes, as usual, distance to a nearest integer.
Publication Year: 2019
Publication Date: 2019-11-26
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 1
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot