On the representation of integers as a sum of mixed powers
type: Item
instance of: scholarly article
title: On the representation of integers as a sum of mixed powers
zbMATH Open document ID: 0849.11073
DOI: 10.1007/BF02303970
author: A. M. Dashkevich
published in: Mathematical Notes
publication date: 1996-02-21T00:00:00Z
review text: The author uses the Hardy-Littlewood method to establish an asymptotic formula for the number of representations of a large number in the form \(n^2_1+ n^3_2+ n^3_3+ n^3_4+ n^3_5+ n^6_6+ n^8_7\). This extends results of \textit{M. Lu} [Acta Arith. 58, 89-102 (1991; Zbl 0725.11050)], in whose work at least one of \(n_6\), \(n_7\) appeared to a lower degree. The formula assumes the shape \(c\sigma (n) n^{73/72}+ O(n^{73/ 72-\delta})\), where \(\delta>0\) and \(\sigma (n)\) denotes a ``singular series''. (The exponent \(\delta\) is however typeset as \(\sigma\)).
reviewed by: George Greaves
Mathematics Subject Classification ID: 11P05
Mathematics Subject Classification ID: 11P55
zbMATH DE Number: 846496
zbMATH Keywords: sums of mixed powers
zbMATH Keywords: Hardy-Littlewood method
zbMATH Keywords: asymptotic formula
zbMATH Keywords: singular series
zbMATH Keywords: representations of large numbers
MaRDI profile type: Publication
cites work: On a problem of sums of mixed powers
cites work: A problem in additive number theory
cites work: Sums of Three Cubes
full work available at URL: https://doi.org/10.1007/bf02303970
OpenAlex ID: W1993287854
description: scientific article; zbMATH DE number 846496