Abstract
This paper concerns systems of r homogeneous diagonal equations of degree k in s variables, with integer coefficients. Subject to a suitable non-singularity condition, it is shown that the expected asymptotic formula holds for the number of such systems inside a box [-P, P](s), provided only that s > (3r + 1)2(k-2). By way of comparison, classical methods based on the use of Hua's lemma would establish a similar conclusion, provided instead that s > r2(k).
| Translated title of the contribution | Hua's lemma and simultaneous diagonal equations |
|---|---|
| Original language | English |
| Pages (from-to) | 279 - 283 |
| Number of pages | 5 |
| Journal | Bulletin of the London Mathematical Society |
| Volume | 34 (3) |
| DOIs | |
| Publication status | Published - May 2002 |