The asymptotic formula in Waring's problem: higher order expansions

Abstract

When k > 1 and s is sufficiently large in terms of k, we derive an explicit multi-term asymptotic expansion for the number of representations of a large natural number as the sum of s positive integral k-th powers.

References in corpus (2)

• Vinogradov's mean value theorem via efficient congruencing, II
• Multigrade efficient congruencing and Vinogradov's mean value theorem

Cited by in corpus (3)

• Secondary terms in asymptotics for the number of zeros of quadratic forms over number fields
• Invariant four-variable automorphic kernel functions
• Integer points on homogeneous varieties with two or more degrees