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Febuary 2020 Waring–Goldbach problem: two squares and three biquadrates
Li Zhu
Rocky Mountain J. Math. 50(1): 355-367 (Febuary 2020). DOI: 10.1216/rmj.2020.50.355

Abstract

Let (n) denote the number of representations of the positive integer n as the sum of two squares and three biquadrates of primes and we write (N) for the number of positive integers n satisfying nN, n5,53,101(mod120) and

| ( n ) Γ 2 ( 1 2 ) Γ 3 ( 1 4 ) Γ ( 7 4 ) 𝔖 ( n ) n 3 4 log 5 n | n 3 4 log 1 1 2 n ,

where 0<𝔖(n)1 is the singular series. In this paper, we prove

( N ) N 1 5 3 2 + 𝜀

for any 𝜀>0. This result constitutes a refinement upon that of Friedlander and Wooley (2014).

Citation

Download Citation

Li Zhu. "Waring–Goldbach problem: two squares and three biquadrates." Rocky Mountain J. Math. 50 (1) 355 - 367, Febuary 2020. https://doi.org/10.1216/rmj.2020.50.355

Information

Received: 13 February 2019; Revised: 12 August 2019; Accepted: 14 August 2019; Published: Febuary 2020
First available in Project Euclid: 30 April 2020

zbMATH: 07201571
MathSciNet: MR4092561
Digital Object Identifier: 10.1216/rmj.2020.50.355

Subjects:
Primary: 11P05, 11P55

Rights: Copyright © 2020 Rocky Mountain Mathematics Consortium

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Vol.50 • No. 1 • Febuary 2020
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