Prime Hasse principles via Diophantine second moments

Victor Y. Wang

doi:10.56994/jamr.003.001.001

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arXiv · 2304.08674

Prime Hasse principles via Diophantine second moments

Victor Y. Wang

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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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Victor Y. Wang. 2023-04-18. Prime Hasse principles via Diophantine second moments. https://doi.org/10.56994/jamr.003.001.001

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