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Zhao, Lilu

On the Waring-Goldbach problem for fourth and sixth powers. (English) Zbl 1370.11116

Proc. Lond. Math. Soc. (3) 108, No. 6, 1593-1622 (2014).
Summary: We consider the Waring-Goldbach problem for fourth and sixth powers. In particular, we establish that every sufficiently large positive integer under a natural congruence condition can be represented as a sum of \(13\) fourth powers of prime numbers. This improves upon the earlier result of K. Kawada and T. D. Wooley [Proc. Lond. Math. Soc. (3) 83, No. 1, 1–50 (2001; Zbl 1016.11046)].

Cited in 5 Reviews
Cited in 37 Documents

MSC:

11P05 Waring’s problem and variants
11P55 Applications of the Hardy-Littlewood method
11L03 Trigonometric and exponential sums (general theory)

Keywords:

Waring-Goldbach problem; fourth power; sixth power; Hardy-Littlewood method

Citations:

Zbl 1016.11046
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\textit{L. Zhao}, Proc. Lond. Math. Soc. (3) 108, No. 6, 1593--1622 (2014; Zbl 1370.11116)
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