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Sums of three cubes, II

Volume 170 / 2015

Trevor D. Wooley Acta Arithmetica 170 (2015), 73-100 MSC: 11P05, 11L15, 11P55. DOI: 10.4064/aa170-1-6

Abstract

Estimates are provided for $s$th moments of cubic smooth Weyl sums, when $4\le s\le 8$, by enhancing the author's iterative method that delivers estimates beyond classical convexity. As a consequence, an improved lower bound is presented for the number of integers not exceeding $X$ that are represented as the sum of three cubes of natural numbers.

Authors

  • Trevor D. WooleySchool of Mathematics
    University of Bristol
    University Walk, Clifton
    Bristol BS8 1TW, United Kingdom
    e-mail

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