Hardy Ramanujan Journal |

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.

Source : oai:HAL:hal-01986722v1

Published on: January 23, 2019

Submitted on: January 23, 2019

Keywords: Selberg's sieve,Brun-Titchmarsh theorem,arithmetic progressions 2010 Mathematics Subject Classification Primary 11N37,11N13,Secondary 11B25,11N35,11N69,
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MATH
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Mathematics [math],
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MATH.MATH-NT
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Mathematics [math]/Number Theory [math.NT]