eng
episciences.org
Hardy-Ramanujan Journal
2804-7370
2019-01-23
10.46298/hrj.2019.5118
5118
journal article
The Barban-Vehov Theorem in Arithmetic Progressions
V Kumar Murty
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://hrj.episciences.org/5118/pdf
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]