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Journal Articles Hardy-Ramanujan Journal Year : 2019

The Barban-Vehov Theorem in Arithmetic Progressions


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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hal-01986722 , version 1 (19-01-2019)



V Kumar Murty. The Barban-Vehov Theorem in Arithmetic Progressions. Hardy-Ramanujan Journal, 2019, Atelier Digit_Hum, pp.157 - 171. ⟨10.46298/hrj.2019.5118⟩. ⟨hal-01986722⟩


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