Waring's problem for cubes is investigated using numerical computations. The densities of number not representable as a sum of four and five cubes are computed in large intervals. Extrapolation of these data allows us to conjecture on the order of magnitude of last exceptions. The representability with four relative cubes and the validity of the theoretical asymptotic formula are investigated too. All the results reasonably confirm the conjecture that four relative cubes suffice to represent any integer and four nonnegative cubes suffice to represent any «large» integer.

Computations Concerning Waring's Problem for Cubes

ROMANI, FRANCESCO
1982-01-01

Abstract

Waring's problem for cubes is investigated using numerical computations. The densities of number not representable as a sum of four and five cubes are computed in large intervals. Extrapolation of these data allows us to conjecture on the order of magnitude of last exceptions. The representability with four relative cubes and the validity of the theoretical asymptotic formula are investigated too. All the results reasonably confirm the conjecture that four relative cubes suffice to represent any integer and four nonnegative cubes suffice to represent any «large» integer.
1982
Romani, Francesco
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/7142
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 5
  • ???jsp.display-item.citation.isi??? ND
social impact