On Roth's theorem concerning a cube and three cubes of primes

X. Ren

Type: Article

Publication Date: 2004-09-01

Citations: 3

DOI: https://doi.org/10.1093/qmath/hah002

Abstract

In this paper, we prove that with at most O(N1271/1296+ε) exceptions, all positive integers up to N are the sum of a cube and three cubes of primes. This improves an earlier result O(N169/170) of the first author and the classical result O(NL‐A) of Roth.

Locations

The HKU Scholars Hub (University of Hong Kong) - View - PDF
The Quarterly Journal of Mathematics - View

Similar Works

Action	Title	Year	Authors
+	On Roth's theorem concerning a cube and three cubes of primes	2004	X. Ren
+	The exceptional set in Roth's theorem concerning a cube and three cubes of primes	2001	X. Ren
+	The Additive Problem with One Cube and Three Cubes of Primes	2014	Lilu Zhao
+	ON SUMS OF TWO PRIME SQUARES, FOUR PRIME CUBES AND POWERS OF TWO	2020	Yuhui Liu
+	2348. A simple proof that all large integers are sums of at most eight cubes	1953	G. L. Watson
+	An explicit result of the sum of seven cubes	2007	Olivier Ramaré
+	On squares of sums of three cubes	2020	Javier Pliego
+	On the representation of an even perfect number as the sum of a limited number of cubes	2015	Bakir Farhi
+ PDF Chat	On an inequality in a 1970 paper of R. L. Graham	2022	J.-P. Allouche
+	Sums of five cubes of primes	2009	Hiroshi Mikawa T. P. Peneva
+	Sum of cubes: Old proofs suggest new q-analogues	2014	Johann Cigler
+	Sum of cubes: Old proofs suggest new q-analogues	2014	Johann Cigler
+	Improving Roth's theorem in the primes	2009	H. A. Helfgott Anne de Roton
+ PDF Chat	Improving Roth's Theorem in the Primes	2010	H. A. Helfgott Anne de Roton
+	A diophantine problem concerning cubes	2005	Ajai Choudhry
+	Cube sum problem for integers having exactly two distinct prime factors	2022	Dipramit Majumdar Pratiksha Shingavekar
+	Goldbach-Linnik type problems involving one prime, four prime cubes and powers of 2	2023	Han Xue Huafeng Liu
+ PDF Chat	On representation of integers by sums of a cube and three cubes of primes	2005	Xiumin Ren Kai-Man Tsang
+	Note on the sum of cubes of primes and an almost prime	1997	Koichi Kawada
+	A Conjecture On Primes	2005	LE Mao-hua

Works That Cite This (3)

Action	Title	Year	Authors
+	The Additive Problem with One Cube and Three Cubes of Primes	2014	Lilu Zhao
+	A result on Waring–Goldbach problem for cubes	2011	Zhixin Liu
+ PDF Chat	On representation of integers by sums of a cube and three cubes of primes	2005	Xiumin Ren Kai-Man Tsang

Works Cited by This (14)

Action	Title	Year	Authors
+	Multiplicative Number Theory	1980	H. Davenport
+ PDF Chat	Large values of Dirichlet polynomials, III	1975	M. N. Huxley
+	Topics in Multiplicative Number Theory	1971	Hugh L. Montgomery
+	The exceptional set in Roth's theorem concerning a cube and three cubes of primes	2001	X. Ren
+ PDF Chat	On Waring’s problem for cubes	1939	H. Davenport
+	On Waring's Problem for Cubes	1951	K. F. Roth
+	SOME RESULTS IN THE ADDITIVE PRIME-NUMBER THEORY	1938	Loo-Keng Hua
+	On Lagrange's Theorem with Prime Variables	2003	Jing Liu
+	The Theory of the Riemann Zeta-Function	1987	E. C. Titchmarsh D. R. Heath‐Brown
+	On the Additive Theory of Prime Numbers	2008	Patrick Cégielski Denis Richard Maxim Vsemirnov