A variant of the Bombieri-Vinogradov theorem with explicit constants and applications
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- by Amir Akbary and Kyle Hambrook PDF
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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.References
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Additional Information
- Amir Akbary
- Affiliation: Department of Mathematics and Computer Science, University of Lethbridge, Lethbridge, AB T1K 3M4 Canada
- MR Author ID: 650700
- Email: amir.akbary@uleth.ca
- Kyle Hambrook
- Affiliation: Department of Mathematics, 1984 Mathematics Road, University of British Columbia, Vancouver, BC V6T 1Z2 Canada
- MR Author ID: 952267
- ORCID: 0000-0002-0097-4257
- Email: hambrook@math.ubc.ca
- 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
- © Copyright 2014 American Mathematical Society
- Journal: Math. Comp. 84 (2015), 1901-1932
- MSC (2010): Primary 11N13
- DOI: https://doi.org/10.1090/S0025-5718-2014-02919-0
- MathSciNet review: 3335897