Frontiers of Mathematics in China >

2020 , Vol. 15 >Issue 1: 183 - 204

DOI: https://doi.org/10.1007/s11464-020-0820-6

RESEARCH ARTICLE

Second moment of error term of mean value for binary Egyptian fractions

  • Xuanxuan XIAO , 1 ,
  • Wenguang ZHAI 2
Expand
  • 1. Faculty of Information Technology, Macau University of Science and Technology, Macau, China
  • 2. Department of Mathematics, China University of Mining and Technology, Beijing 100083, China

Received date: 23 Nov 2019

Accepted date: 30 Jan 2020

Published date: 15 Feb 2020

Copyright

2020 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
Fold

Abstract

We study the mean square of the error term of the mean value for binary Egyptian fractions. We get an asymptotic formula under the Riemann Hypothesis.

Key words： Binary Egyptian fractions; mean values; error terms

Cite this article

Xuanxuan XIAO , Wenguang ZHAI . Second moment of error term of mean value for binary Egyptian fractions[J]. Frontiers of Mathematics in China, 2020 , 15(1) : 183 -204 . DOI: 10.1007/s11464-020-0820-6

References

Publishing order | Descend order by publishing year | Descend order by cited within
1
Cao X, Tanigawa Y, Zhai W. Tong-type identity and the mean square of the error term for an extended Selberg class. Sci China Math, 2016, 59: 2103–2144

DOI

2
Furuya J, Zhai W. On the -free divisor problem. Acta Arith, 2006, 123: 267–287

DOI

3
Furuya J, Zhai W. On the -free divisor problem (II). Acta Arith, 2008, 132: 351–358

DOI

4
Huang J, Vaughan R C. Mean value theorems for binary Egyptian fractions. Acta Arith, 2011, 155: 287–296

DOI

5
Huang J, Vaughan R C. Mean value theorems for binary Egyptian fractions II. J Number Theory, 2011, 131: 1641–1656

DOI

6
Huang J, Vaughan R C. On the exceptional set for binary Egyptian fractions. Bull Lond Math Soc, 2013, 45: 861–874

DOI

7
Ivić A. The Riemann Zeta-Function. New York: Wiley, 1985

8
Jia C. Mean value from representation of rational number as sum of two Egyptian fractions. J Number Theory, 2012, 132: 701–713

DOI

9
Montgomery H L, Vaughan R C. On the distribution of square free numbers. In: Recent Progress in Analytic Number Theory I. London: Academic Press, 1981, 247–256

10
Montgomery H L, Vaughan R C. Multiplicative Number Theory I. Classical Theory. Cambridge: Cambridge Univ Press, 2007

DOI

11
Xiao X, Zhai W. Error term of the mean value theorem for binary Egyptian fractions. Preprint

Options
Outlines

/

〈 〉