Abstract
In this paper we prove that, with at most $O(N^{13/15+\varepsilon})$ exceptions, all positive even integers $n \leq N$ with $n \equiv 4 (\mathrm{mod}\,24)$ can be written as sums of four squares of primes.
Citation
Jianya Liu. Ming-Chit Liu. "The exceptional set in the four prime squares problem." Illinois J. Math. 44 (2) 272 - 293, Summer 2000. https://doi.org/10.1215/ijm/1255984841
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