Some sums involving Farey fractions II
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概要
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Let F<SUB>x</SUB> denote the Farey series of order [x], i.e. the increasing sequence of irreducible fractions ρ<SUB>v</SUB>∈(0, 1] whose denominators do not exceed x. We shall obtain precise asymptotic formulae for the sum \displaystyle ∑_{v=1}<SUP>¶hi(x)</SUP>ρ<SUB>v</SUB><SUP>Z</SUP> for complex z and related sums, ¶hi(x)=\# F<SUB>x</SUB> coinciding the summatory function of Eulers function. In particular, we shall prove an asymptotic formula for \displaystyle ∑ρ<SUB>v</SUB><SUP>-1</SUP> with as good an estimate as for the prime number theorem by extracting an intermediate error term occurring in the asymptotic formula for ¶hi(x).
- 社団法人 日本数学会の論文
- 2000-10-01
著者
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Kanemitsu Shigeru
Department Of Electrical Engineering University Of Kinki
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吉元 昌己
日本学術振興会特別研究院(pd)
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吉元 昌己
名古屋大学多元数理科学研究科
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吉元 昌巳
九州大学
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Yoshimoto Masami
Graduate School Of Mathematics Nagoya University
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Yoshimoto Masami
Graduate School Of Mathematics Kyushu University
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KUZUMAKI Takako
Department of Electrical Engineering Faculty of Engineering Gifu University
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