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The Barban-Vehov Theorem in Arithmetic Progressions

Abstract : 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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Submitted on : Saturday, January 19, 2019 - 9:26:44 AM
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V Kumar Murty. The Barban-Vehov Theorem in Arithmetic Progressions. Hardy-Ramanujan Journal, Hardy-Ramanujan Society, 2019, Atelier Digit_Hum, pp.157 - 171. ⟨10.46298/hrj.2019.5118⟩. ⟨hal-01986722⟩

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