Representation of integers as monochromatic sums of squares of primes

Authors

Kummari Mallesham, Indian Statistical Institute, Kolkata
Gyan Prakash, Harish Chandra Research Institute
D. S. Ramana, Harish Chandra Research Institute

Article Type

Research Article

Publication Title

Journal of Number Theory

Abstract

For any integer K≥1, let s(K) be the smallest integer such that when the set of squares of the prime numbers is coloured in K colours, 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 [Formula presented] for K≥2. This upper bound for s(K) is close to optimal and improves on s(K)≪ϵK2+ϵ, which is the best available upper bound for s(K).

First Page

102

Last Page

119

DOI

10.1016/j.jnt.2020.11.020

Publication Date

2-1-2022

Recommended Citation

Mallesham, Kummari; Prakash, Gyan; and Ramana, D. S., "Representation of integers as monochromatic sums of squares of primes" (2022). Journal Articles. 3284.
https://digitalcommons.isical.ac.in/journal-articles/3284