Goldbach-Waring problem
From Encyclopedia of Mathematics
Revision as of 18:52, 24 March 2012 by Ulf Rehmann (talk | contribs) (moved Goldbach–Waring problem to Goldbach-Waring problem: ascii title)
A problem concerning the behaviour of the number of solutions 
of the equation
 |
where 
are prime numbers and 
(cf. Waring problem; Goldbach problem). The results obtained (up to 1977) are roughly the same as those obtained in Waring's problem: It has been proved that the equation is solvable (i.e. 
) if 
, while an asymptotic formula for 
has been obtained for 
. These solutions were obtained by the Vinogradov method.
References
| [1] | I.M. Vinogradov, "The method of trigonometric sums in the theory of numbers" , Interscience (1954) (Translated from Russian) |
| [2] | L.-K. Hua, "Abschätzungen von Exponentialsummen und ihre Anwendung in der Zahlentheorie" , Enzyklopaedie der Mathematischen Wissenschaften mit Einschluss ihrer Anwendungen , 1 : 2 (1959) (Heft 13, Teil 1) |
How to Cite This Entry:
Goldbach-Waring problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Goldbach-Waring_problem&oldid=22519
Goldbach-Waring problem. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Goldbach-Waring_problem&oldid=22519
This article was adapted from an original article by A.A. Karatsuba (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article