Second moment of error term of mean value for binary Egyptian fractions
Xuanxuan XIAO, Wenguang ZHAI
Second moment of error term of mean value for binary Egyptian fractions
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.
Binary Egyptian fractions / mean values / error terms
[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
CrossRef
Google scholar
|
[2] |
Furuya J, Zhai W. On the
CrossRef
Google scholar
|
[3] |
Furuya J, Zhai W. On the
CrossRef
Google scholar
|
[4] |
Huang J, Vaughan R C. Mean value theorems for binary Egyptian fractions. Acta Arith, 2011, 155: 287–296
CrossRef
Google scholar
|
[5] |
Huang J, Vaughan R C. Mean value theorems for binary Egyptian fractions II. J Number Theory, 2011, 131: 1641–1656
CrossRef
Google scholar
|
[6] |
Huang J, Vaughan R C. On the exceptional set for binary Egyptian fractions. Bull Lond Math Soc, 2013, 45: 861–874
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[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
CrossRef
Google scholar
|
[11] |
Xiao X, Zhai W. Error term of the mean value theorem for binary Egyptian fractions. Preprint
|
/
〈 | 〉 |