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Annales mathématiques du Québec

, Volume 39, Issue 2, pp 121–128 | Cite as

\(\kappa \)-Factor in arithmetic progressions

  • Olivier BordellèsEmail author
Article
  • 72 Downloads

Abstract

Introducing the concept of \(\kappa \)-factor function generalizing the well-known irrational factor function, we refine a previous estimate given by S. Chaubey, M. Lanius and A. Zaharescu for the irrational factor function in arithmetic progressions. In particular, the dependence in q in the error term is explicited. An asymptotic formula for the \(\kappa \)-factor function on shifted primes is also given.

Keywords

\(\kappa \)-Factor function Dirichlet characters Pólya–Vinogradov’s inequality 

Résumé

Après avoir défini la notion de fonction \(\kappa \)-facteur, qui généralise celle de facteur irrationnel, nous améliorons un résultat obtenu par S. Chaubey, M. Lanius and A. Zaharescu concernant l’ordre moyen de la fonction facteur irrationnel en progressions arithmétiques. En particulier, la dépendance en q du terme d’erreur est explicitée. Une formule asymptotique pour la fonction \(\kappa \)-facteur sur les nombres premiers décalés est également fournie.

Mathematics Subject Classification

11A25 11N37 11M06 

Notes

Acknowledgments

I am gratefully indebted to the anonymous referee who carefully read a previous version of the manuscript and suggested to study the mean value of \(F_\kappa \) on the set of shifted primes.

References

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Copyright information

© Fondation Carl-Herz and Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.AiguilheFrance

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