Diophantine approximation over primes with different powers
作者：
Highlights：
• We determine an upper bound for the quantity of real numbers in a well spaced sequence making the Diophantine approximation over two squares, two cubes and two biquadrates of primes unsolvable.
• We prove that under some specific conditions, the values of real linear combinations of two squares, two cubes and two biquadrates of primes can approximate almost all real numbers in a well spaced sequence.
• Our results extend some recent publications.
摘要
•We determine an upper bound for the quantity of real numbers in a well spaced sequence making the Diophantine approximation over two squares, two cubes and two biquadrates of primes unsolvable.•We prove that under some specific conditions, the values of real linear combinations of two squares, two cubes and two biquadrates of primes can approximate almost all real numbers in a well spaced sequence.•Our results extend some recent publications.
论文关键词：Diophantine approximation,Sieve function,Prime
论文评审过程：Received 28 July 2021, Revised 6 January 2022, Accepted 8 January 2022, Available online 24 January 2022, Version of Record 24 January 2022.
论文官网地址：https://doi.org/10.1016/j.amc.2022.126940
