{"docId":5118,"paperId":5118,"url":"https:\/\/hrj.episciences.org\/5118","doi":"10.46298\/hrj.2019.5118","journalName":"Hardy-Ramanujan Journal","issn":"","eissn":"2804-7370","volume":[],"section":[],"repositoryName":"Hal","repositoryIdentifier":"hal-01986722","repositoryVersion":1,"repositoryLink":"https:\/\/hal.science\/hal-01986722v1","dateSubmitted":"2019-01-23 14:23:01","dateAccepted":"2019-01-23 15:41:19","datePublished":"2019-01-23 15:41:30","titles":{"en":"The Barban-Vehov Theorem in Arithmetic Progressions"},"authors":["Kumar Murty , V"],"abstracts":{"en":"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."},"keywords":[["Selberg's sieve"],["Brun-Titchmarsh theorem"],["arithmetic progressions 2010 Mathematics Subject Classification Primary 11N37"],["11N13"],["Secondary 11B25"],["11N35"],["11N69"],"[ MATH ] Mathematics [math]","[ MATH.MATH-NT ] Mathematics [math]\/Number Theory [math.NT]"]}