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Density Bounds in Hua's Theorem for Prime Squares

Michael T. Lacey, Hamed Mousavi, Yaghoub Rahimi, Manasa N. Vempati

Source record

Source: arXiv

Published: Oct 15, 2026

arXiv: 2610.22747

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Source abstract

We prove a density version of Hua's theorem in the five-variable case: if P\mathcal P is a subset of the primes with relative lower density greater than 0.820.82, then every sufficiently large n≡5(mod24)n\equiv5\pmod{24} is a sum of five squares of primes from P\mathcal P.

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