V Kumar Murty - The Barban-Vehov Theorem in Arithmetic Progressions

hrj:5118 - Hardy-Ramanujan Journal, January 23, 2019 - https://doi.org/10.46298/hrj.2019.5118
The Barban-Vehov Theorem in Arithmetic ProgressionsArticle

Authors: V Kumar Murty 1

  • 1 Department of Mathematics [University of Toronto]


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.

https://doi.org/10.46298/hrj.2019.5118
Source: HAL:hal-01986722v1
Published on: January 23, 2019
Imported on: January 23, 2019
Keywords: [MATH]Mathematics [math], [MATH.MATH-NT]Mathematics [math]/Number Theory [math.NT], [en] Selberg's sieve, Brun-Titchmarsh theorem, arithmetic progressions 2010 Mathematics Subject Classification Primary 11N37, 11N13, Secondary 11B25, 11N35, 11N69

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