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Prime Hasse principles via Diophantine second moments
Published 18 Apr 2023 in math.NT and math.AG | (2304.08674v2)
Abstract: We show that almost all primes $p\not\equiv \pm 4 \bmod{9}$ are sums of three cubes, assuming a conjecture due to Hooley, Manin, et al. on cubic fourfolds. This conjecture is approachable under standard statistical hypotheses on geometric families of $L$-functions.
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