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

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)].

### MSC:

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

Zbl 1016.11046
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