Hua’s theorem on five squares of primes

Wenjia ZHAO

Front. Math. China ›› 2020, Vol. 15 ›› Issue (4) : 835 -850.

PDF (312KB)
Front. Math. China ›› 2020, Vol. 15 ›› Issue (4) : 835 -850. DOI: 10.1007/s11464-020-0851-z
RESEARCH ARTICLE
RESEARCH ARTICLE

Hua’s theorem on five squares of primes

Author information +
History +
PDF (312KB)

Abstract

We give an alternative proof of Hua’s theorem that each large N5 (mod 24) can be written as a sum of five squares of primes. The proof depends on an estimate of exponential sums involving the Möbius function.

Keywords

Exponential sums / Hua’s theorem / Möbius function

Cite this article

Download citation ▾
Wenjia ZHAO. Hua’s theorem on five squares of primes. Front. Math. China, 2020, 15(4): 835-850 DOI:10.1007/s11464-020-0851-z

登录浏览全文

4963

注册一个新账户 忘记密码

References

[1]

Brüdern J, Fouvry E. Lagrange’s four squares theorem with almost prime variables. J Reine Angew Math, 1994, 454: 59–96

[2]

Davenport H. On some infinite series involving arithmetical functions (II). Quart J Math (Oxford), 1937, 8: 313–320

[3]

Hua L K. Some results in the additive prime number theory. Quart J Math (Oxford), 1938, 9: 68–80

[4]

Hua L K. Additive Theory of Prime Numbers. Transl Math Monogr, Vol 13. Providence: Amer Math Soc, 1965

[5]

Iwaniec H, Kowalski E. Analytic Number Theory. Amer Math Soc Colloq Publ, Vol 53. Providence: Amer Math Soc, 2004

[6]

Liu J Y. On Lagrange’s theorem with prime variables. Quart J Math (Oxford), 2002, 54: 453–467

[7]

Liu J Y, Liu M C. The exceptional set in the four prime squares problem. Illinois J Math, 2000, 44: 272–293

[8]

Liu J Y, Liu M C, Zhan T. Squares of primes and powers of 2 (English summary). Monatsh Math, 1999, 128(4): 283–313

[9]

Liu J Y, Wooley T D, Yu G. The quadratic Waring-Goldbach problem. J Number Theory, 2004, 107(2): 298–321

[10]

Ren X M. On exponential sum over primes and application in Waring-Goldbach problem. Sci China Ser A Math, 2005, 48(6): 785–797

[11]

Schwarz W. Zur Darstellung von Zahlen durch Summen von Primzahlpotenzen II. J Reine Angew Math, 1961, 206: 78–112

RIGHTS & PERMISSIONS

Higher Education Press

AI Summary AI Mindmap
PDF (312KB)

999

Accesses

0

Citation

Detail

Sections
Recommended

AI思维导图

/