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Article Dans Une Revue Hardy-Ramanujan Journal Année : 1989

An Ω-result related to r4(n).

Résumé

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 Erd\"os 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
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Dates et versions

hal-01104372 , version 1 (16-01-2015)

Identifiants

Citer

Sukumar Das Adhikari, R Balasubramanian, A Sankaranarayanan. An Ω-result related to r4(n).. Hardy-Ramanujan Journal, 1989, Volume 12 - 1989, pp.29 - 30. ⟨10.46298/hrj.1989.113⟩. ⟨hal-01104372⟩
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