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The Barban-Vehov Theorem in Arithmetic Progressions
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A result of Barban-Vehov (and independently Motohashi) gives an estimate for the mean square of a sequence related to Selberg's sieve. This upper bound was refined to an asymptotic formula by S. Graham in 1978. In 1992, I made the observation that Graham's method can be used to obtain an asymptotic formula when the sum is restricted to an arithmetic progression. This formula immediately gives a version of the Brun-Titchmarsh theorem. I am taking the occasion of a volume in honour of my friend S. Srinivasan to revisit and publish this observation in the hope that it might still be of interest.
Title: The Barban-Vehov Theorem in Arithmetic Progressions
Description:
A result of Barban-Vehov (and independently Motohashi) gives an estimate for the mean square of a sequence related to Selberg's sieve.
This upper bound was refined to an asymptotic formula by S.
Graham in 1978.
In 1992, I made the observation that Graham's method can be used to obtain an asymptotic formula when the sum is restricted to an arithmetic progression.
This formula immediately gives a version of the Brun-Titchmarsh theorem.
I am taking the occasion of a volume in honour of my friend S.
Srinivasan to revisit and publish this observation in the hope that it might still be of interest.
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