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

doi:10.1007/s11464-020-0820-6

Front. Math. China

2020, Vol. 15

Issue (1) : 183-204 https://doi.org/10.1007/s11464-020-0820-6

RESEARCH ARTICLE

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

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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.

Keywords Binary Egyptian fractions mean values error terms

Corresponding Author(s): Xuanxuan XIAO

Issue Date: 09 March 2020

Cite this article:

Xuanxuan XIAO,Wenguang ZHAI. Second moment of error term of mean value for binary Egyptian fractions[J]. Front. Math. China, 2020, 15(1): 183-204.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0820-6
https://academic.hep.com.cn/fmc/EN/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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