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We apply multigrade efficient congruencing to estimate Vino- gradov's integral of degree k for moments of order 2s, establishing strongly diagonal behaviour for 1 6 s 6 1 k(k +… Click to show full abstract
We apply multigrade efficient congruencing to estimate Vino- gradov's integral of degree k for moments of order 2s, establishing strongly diagonal behaviour for 1 6 s 6 1 k(k + 1) − 1 k + o(k). In particular, as k → ∞, we confirm the main conjecture in Vinogradov's mean value theorem for 100% of the critical interval 1 6 s 6 1 k(k + 1).
Keywords:
vinogradov mean;
value theorem;
conjecture vinogradov;
main conjecture;
mean value
Journal Title: Mathematika
Year Published: 2017
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Journal Title: Mathematika
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!