By avoiding a conventional application of Besselâ€™s inequality in favour of explicitly controlling an exponential sum over the exceptional set, in our previous work [9, 10], we have exploited additional variables so as to enhance exceptional set estimates in various additive problems of Waring type. In this paper we turn to the problem of establishing the expected asymptotic formula in Waringâ€™s problem. The methods introduced herein, although discussed in the context of the asymptotic formula, should nonetheless provide a useful model for future excursions involving exceptional sets in additive problems.
|Translated title of the contribution||Slim exceptional sets and the asymptotic formula in Waring's problem|
|Pages (from-to)||193 - 206|
|Number of pages||14|
|Journal||Mathematical Proceedings of the Cambridge Philosophical Society|
|Publication status||Published - 2 May 2003|