Publication at Faculty of Mathematics and Physics |
2022
Abstract
A positive quadratic form is (k, l)-universal if it represents all the numbers kx + l where x is a non-negative integer, and almost (k, l)-universal if it represents all but finitely many of them. We prove that for any k, l & nbsp;such that k { 8 there exists an almost (k, .l)-universal diagonal ternary form.
We also conjecture that there are only finitely many primes p for which a (p, l)-universal diagonal ternary form exists (for any l & nbsp;< p) and we show the results of computer experiments that speak in favor of the conjecture.(C) 2021 Elsevier Inc. All rights reserved.