Multigrade efficient congruencing and Vinogradov's mean value theorem Article Swipe

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Trevor D. Wooley ·

YOU? · · 2015 · Open Access · · DOI: https://doi.org/10.1112/plms/pdv034 · OA: W1904038357

We develop a multigrade enhancement of the efficient congruencing method to estimate Vinogradov's integral of degree $k$ for moments of order $2s$, thereby obtaining near-optimal estimates for $\tfrac{5}{8}k^21.543k^2$. The asymptotic formula is also established for sums of $28$ fifth powers.

Multigrade efficient congruencing and Vinogradov's mean value theorem Article Swipe

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