Sukumar Das Adhikari ; R Balasubramanian ; A Sankaranarayanan - An Ω-result related to r4(n).

hrj:113 - Hardy-Ramanujan Journal, January 1, 1989, Volume 12 - 1989 - https://doi.org/10.46298/hrj.1989.113
An Ω-result related to r4(n).Article

Authors: Sukumar Das Adhikari 1; R Balasubramanian 1; A Sankaranarayanan 2

Let r4(n) be the number of ways of writing n as the sum of four squares. Set P4(x)=nxr4(n)12π2x2, the error term for the average order of this arithmetical function. In this paper, following the ideas of Erdös and Shapiro, a new elementary method is developed which yields the slightly stronger result P4(x)=Ω+(xloglogx). We also apply our method to give an upper bound for a quantity involving the Euler φ-function. This second result gives an elementary proof of a theorem of H. L. Montgomery


Volume: Volume 12 - 1989
Published on: January 1, 1989
Imported on: March 3, 2015
Keywords: Omega results of the error terms,arithmetical functions,[MATH]Mathematics [math]

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