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Frontiers of Mathematics in China

ISSN 1673-3452

ISSN 1673-3576(Online)

CN 11-5739/O1

邮发代号 80-964

2019 Impact Factor: 1.03

Frontiers of Mathematics in China  2020, Vol. 15 Issue (1): 183-204   https://doi.org/10.1007/s11464-020-0820-6
  本期目录
Second moment of error term of mean value for binary Egyptian fractions
Xuanxuan XIAO1(), Wenguang ZHAI2
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
 全文: PDF(337 KB)  
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 wordsBinary Egyptian fractions    mean values    error terms
收稿日期: 2019-11-23      出版日期: 2020-03-09
Corresponding Author(s): Xuanxuan XIAO   
 引用本文:   
. [J]. Frontiers of Mathematics in China, 2020, 15(1): 183-204.
Xuanxuan XIAO, Wenguang ZHAI. Second moment of error term of mean value for binary Egyptian fractions. Front. Math. China, 2020, 15(1): 183-204.
 链接本文:  
https://academic.hep.com.cn/fmc/CN/10.1007/s11464-020-0820-6
https://academic.hep.com.cn/fmc/CN/Y2020/V15/I1/183
1 X Cao, Y Tanigawa, W Zhai. Tong-type identity and the mean square of the error term for an extended Selberg class. Sci China Math, 2016, 59: 2103–2144
https://doi.org/10.1007/s11425-015-0706-2
2 J Furuya, W Zhai. On the -free divisor problem. Acta Arith, 2006, 123: 267–287
https://doi.org/10.4064/aa123-3-4
3 J Furuya, W Zhai. On the -free divisor problem (II). Acta Arith, 2008, 132: 351–358
https://doi.org/10.4064/aa132-4-4
4 J Huang, R C Vaughan. Mean value theorems for binary Egyptian fractions. Acta Arith, 2011, 155: 287–296
https://doi.org/10.4064/aa155-3-5
5 J Huang, R C Vaughan. Mean value theorems for binary Egyptian fractions II. J Number Theory, 2011, 131: 1641–1656
https://doi.org/10.1016/j.jnt.2011.04.001
6 J Huang, R C Vaughan. On the exceptional set for binary Egyptian fractions. Bull Lond Math Soc, 2013, 45: 861–874
https://doi.org/10.1112/blms/bdt020
7 A Ivić. The Riemann Zeta-Function. New York: Wiley, 1985
8 C Jia. Mean value from representation of rational number as sum of two Egyptian fractions. J Number Theory, 2012, 132: 701–713
https://doi.org/10.1016/j.jnt.2011.09.007
9 H L Montgomery, R C Vaughan. On the distribution of square free numbers. In: Recent Progress in Analytic Number Theory I. London: Academic Press, 1981, 247–256
10 H L Montgomery, R C Vaughan. Multiplicative Number Theory I. Classical Theory. Cambridge: Cambridge Univ Press, 2007
https://doi.org/10.1017/CBO9780511618314
11 X Xiao, W Zhai. Error term of the mean value theorem for binary Egyptian fractions. Preprint
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