Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three

Ciprian Demeter; Jean Bourgain; Larry Guth

Proof of the main conjecture in Vinogradov's mean value theorem for degrees higher than three

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arxiv 1512.01565 v3 pith:MJD6XI4T submitted 2015-12-04 math.NT

Jean Bourgain , Ciprian Demeter , Larry Guth This is my paper · ORCID

classification math.NT

keywords conjecturedegreeshighermainmeantheoremthreevalue

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We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three. This will be a consequence of a sharp decoupling inequality for curves

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Arithmetic Symmetry in Ideal Prouhet-Tarry-Escott Solutions
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Symmetric ideal degree-3 PTE solutions are asymptotically counted as (4 log 2 / 3 π²) H³ log H + O(H³) due to the second moment of the sum-of-two-squares representation function.

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