Sums of almost equal prime squares

Hongze Li (1) , Jie Wu (2)

1 Department of Mathematics [Shanghai]
2 Analyse

In this short note, we prove that almost all integers $N$ satisfying $N\equiv 3\,({\rm mod}\,24)$ and $5\nmid N$ or $N\equiv 4\,({\rm mod}\,24)$ is the sum of three or four almost equal prime squares, respectively: $N=p_1^2+\cdots+p_j^2$ with $|p_i-(N/j)^{1/2}|\leq N^{1/2-9/80+\varepsilon}$ for $j=3$ or $4$ and $1\leq i\leq j$.

Mots clés: Quadratic equations; Exponential sums; Circle method

Domaines: Théorie des nombres [math.NT]

Hongze Li, Jie Wu. Sums of almost equal prime squares. Functiones et Approximatio Commentarii Mathematici, 2008, 38, pp.7--23. ⟨hal-00097168⟩