Abstract
In this paper we consider Diophantine Approximation using numbers which are a sum of two odd primes (Goldbach Numbers). We use exponential sums and sieve methods to establish, for any irrational $\alpha$ and arbitrary real $\beta$, that there are infinitely many solutions to \[ ||\alpha n + \beta|| < n^{- \frac56}, n = p_1+p_2, p_j \text{denotes an odd prime}, \] where $||\cdot||$ denotes, as usual, distance to a nearest integer.
Citation
Glyn Harman. "Diophantine approximation with Goldbach numbers." Funct. Approx. Comment. Math. 63 (2) 151 - 163, December 2020. https://doi.org/10.7169/facm/1829
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