10.46298/hrj.2019.5118
https://hrj.episciences.org/5118
Kumar Murty
,
V
V
Kumar Murty
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.
episciences.org
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]
2019-01-23
2019-01-23
2019-01-23
en
journal article
https://hal.archives-ouvertes.fr/hal-01986722v1
2804-7370
https://hrj.episciences.org/5118/pdf
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