On monochromatic representation of sums of squares of primes

2017/10/21 by Mallesham, Kummari, Prakash, Gyan, Ramana, D. S
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1710.07767

Abstract

When the sequences of squares of primes is coloured with K colours, where K ≥ 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) ≪ K exp(\frac(3log 2 + \rm o(1))log Klog log K) for K ≥ 2. This improves on s(K) ≪_ε K^{2 +ε}, which is the best available upper bound for s(K).

Related

• A sum of squares not divisible by a prime
• Avoiding Monochromatic Sequences With Special Gaps
• Sums of Consecutive Prime Squares
• Sums of squares with restrictions involving primes
• Monochromatic configurations induced from the set of sums of two squares