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A variant of the Bombieri-Vinogradov theorem with explicit constants and applications


Authors: Amir Akbary and Kyle Hambrook
Journal: Math. Comp. 84 (2015), 1901-1932
MSC (2010): Primary 11N13
DOI: https://doi.org/10.1090/S0025-5718-2014-02919-0
Published electronically: December 29, 2014
MathSciNet review: 3335897
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Abstract: We give an effective version with explicit constants of a mean value theorem of Vaughan related to the values of $ \psi (y, \chi )$, the twisted summatory function associated to the von Mangoldt function $ \Lambda $ and a Dirichlet character $ \chi $. As a consequence of this result we prove an effective variant of the Bombieri-Vinogradov theorem with explicit constants. This effective variant has the potential to provide explicit results in many problems. We give examples of such results in several number theoretical problems related to shifted primes.


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Additional Information

Amir Akbary
Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB T1K 3M4 Canada
Email: amir.akbary@uleth.ca

Kyle Hambrook
Affiliation: Department of Mathematics, 1984 Mathematics Road, University of British Columbia, Vancouver, BC V6T 1Z2 Canada
Email: hambrook@math.ubc.ca

DOI: https://doi.org/10.1090/S0025-5718-2014-02919-0
Keywords: Bombieri-Vinogradov theorem, divisors of shifted primes
Received by editor(s): February 27, 2013
Received by editor(s) in revised form: November 5, 2013
Published electronically: December 29, 2014
Additional Notes: The research of the authors was partially supported by NSERC and ULRF
Article copyright: © Copyright 2014 American Mathematical Society