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arXiv · 1710.07767

On monochromatic representation of sums of squares of primes

Kummari Mallesham·Gyan Prakash·D. S Ramana
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Abstract

When the sequences of squares of primes is coloured with $K$ colours, where $K \geq 1$ is an integer, let $s(K)$ be the smallest integer such that each sufficiently large integer can be written as a sum of no more than $s(K)$ squares of primes, all of the same colour. We show that $s(K) \ll K \exp\left(\frac{(3\log 2 + {\rm o}(1))\log K}{\log \log K}\right)$ for $K \geq 2$. This improves on $s(K) \ll_{\epsilon} K^{2 +\epsilon}$, which is the best available upper bound for $s(K)$.

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Kummari Mallesham, Gyan Prakash, D. S Ramana. 2017-10-21. On monochromatic representation of sums of squares of primes. https://arxiv.org/abs/1710.07767

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