2 problems

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The four cubes of primes conjecture
Four cubes of primes conjecture. Every sufficiently large integer is the sum of at most four cubes of primes:
Conjectureopenadditive-number-theory prime-cubes waring-goldbacharXiv posted 2 days ago
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Conjectured sharp $mathrm{ell}^p$ range for the discrete Waring--Goldbach maximal function
Maximal-function conjecture. The maximal function $A_*$ should be bounded on $\ell^p(\mathbb{Z}^n)$ for every
Conjectureopenergodic-theory harmonic-analysis waring-goldbacharXiv posted 2 days ago

The four cubes of primes conjecture