On the density version of quadratic Waring's problem and the quadratic Waring--Goldbach problem

2025/08/20 by Lim, Zi Li
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2508.14939

Abstract

We prove a sharp density theorem for quadratic Waring's problem over cyclic groups, when the number of variables is at least 5. Also, we obtain some new improvements on the density version of the quadratic Waring--Goldbach problem over integers.

Citations

• A density theorem for prime squares
• A density version of Waring-Goldbach problem
• A density version of Vinogradov's three primes theorem
• The primes contain arbitrarily long arithmetic progressions
• Sum-free sets in abelian groups
• Roth's theorem in the primes
• On Λ(p)-subsets of squares

Related

• A density version of Waring-Goldbach problem
• Waring-Goldbach problem in short intervals
• A note on Waring's problem
• Exact solutions to Waring's problem for finite fields
• Waring-Goldbach Problem with Piatetski-Shapiro Primes