# Asympotic formulae for pairs of diagonal equations

J Brudern, TD Wooley

Research output: Contribution to journalArticle (Academic Journal)peer-review

4 Citations (Scopus)

## Abstract

Consider a system of diagonal equations $$\sum_{j=1}^sa_{ij}x_j^k=0\quad (1\le i\le r),$$ satisfying the property that the (fixed) integral coefficient matrix $(a_{ij})$ contains no singular $r\times r$ submatrix. A recent paper of the authors [3] establishes that whenever $k\ge 3$ and $s>(3r+1)2^{k-2}$, then the expected asymptotic formula holds for the number $N(P)$ of integral solutions ${\bf x}$ of ($1{\cdot}1$) with $|x_i|\le P$ $(1\le i\le s)$.
Translated title of the contribution Asympotic formulae for pairs of diagonal equations English 227 - 235 7 Mathematical Proceedings of the Cambridge Philosophical Society 137 (1 https://doi.org/10.1017/S0305004103007400 Published - 7 Jul 2004

### Bibliographical note

Publisher: Cambridge Univ Press

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