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DOI; consistent capitalisation
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LSpice
LSpice
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This is a year later after the question was asked but for the sake of completeness, the precise result is proved in the following paper of Davenportfollowing paper of Davenport: On Some Infinite Series Involving Arithmetical Functions (II), The Quarterly Journal of Mathematics, Volume os-8, Issue 1, 1937, Pages 313–320. See Lemma 5 which proves it under the condition that $(a,q)=1$ and lemmaLemma 6 which removes the said condition.

This is a year later after the question was asked but for the sake of completeness, the precise result is proved in the following paper of Davenport: On Some Infinite Series Involving Arithmetical Functions (II), The Quarterly Journal of Mathematics, Volume os-8, Issue 1, 1937, Pages 313–320. See Lemma 5 which proves it under the condition that $(a,q)=1$ and lemma 6 which removes the said condition.

This is a year later after the question was asked but for the sake of completeness, the precise result is proved in the following paper of Davenport: On Some Infinite Series Involving Arithmetical Functions (II), The Quarterly Journal of Mathematics, Volume os-8, Issue 1, 1937, Pages 313–320. See Lemma 5 which proves it under the condition that $(a,q)=1$ and Lemma 6 which removes the said condition.

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user859588
user859588
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This is a year later after the question was asked but for the sake of completeness, the precise result is proved in the following paper of Davenport: On Some Infinite Series Involving Arithmetical Functions (II), The Quarterly Journal of Mathematics, Volume os-8, Issue 1, 1937, Pages 313–320. See Lemma 5 which proves it under the condition that $(a,q)=1$ and lemma 6 which removes the said condition.