Table of Contents
Journal of Numbers
Volume 2014 (2014), Article ID 140840, 13 pages
http://dx.doi.org/10.1155/2014/140840
Research Article

Generations of Correlation Averages

Dipartimento di Matematica e Applicazioni, Università degli Studi di Napoli, Via Cinthia, 80126 Napoli, Italy

Received 5 March 2014; Accepted 28 April 2014; Published 18 June 2014

Academic Editor: Aloys Krieg

Copyright © 2014 Giovanni Coppola and Maurizio Laporta. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. A. Selberg, “On the normal density of primes in small intervals, and the difference between consecutive primes,” Archiv for Mathematik og Naturvidenskab, vol. 47, no. 6, pp. 87–105, 1943. View at Google Scholar
  2. G. Coppola, “On some lower bounds of some symmetry integrals,” Afrika Matematika, vol. 25, no. 1, pp. 183–195, 2014. View at Publisher · View at Google Scholar
  3. A. Ivić, “On the mean square of the divisor function in short intervals,” Journal de Théorie des Nombres de Bordeaux, vol. 21, no. 2, pp. 251–261, 2009. View at Publisher · View at Google Scholar
  4. A. Ivić, The Riemann Zeta-Function, John Wiley & Sons, New York, NY, USA, 1985, 2nd edition, Dover, Mineola, NY, USA, 2003.
  5. S. Baier, T. D. Browning, G. Marasingha, and L. Zhao, “Averages of shifted convolutions of d3(n),” Proceedings of the Edinburgh Mathematical Society. Series II, vol. 55, no. 3, pp. 551–576, 2012. View at Publisher · View at Google Scholar
  6. A. Ivić and J. Wu, “On the general additive divisor problem,” Proceedings of the Steklov Institute of Mathematics, vol. 276, no. 1, pp. 140–148, 2012. View at Publisher · View at Google Scholar
  7. G. Coppola, “On the Selberg integral of the k-divisor function and the 2k-th moment of the Riemann zeta-function,” Institut Mathématique. Publications. Nouvelle Série, vol. 88, no. 102, pp. 99–110, 2010. View at Publisher · View at Google Scholar
  8. A. Ivić, “The general additive divisor problem and moments of the zeta-function,” in New Trends in Probability and Statistics, vol. 4, pp. 69–89, VSP, Utrecht, The Netherlands, 1997. View at Google Scholar
  9. G. Coppola, “On the modified Selberg integral,” http://arxiv.org/abs/1006.1229.
  10. G. Coppola, “On the Correlations, Selberg integral and symmetry of sieve functions in short intervals, III,” http://arxiv.org/abs/1003.0302.
  11. G. Coppola, “On the symmetry of divisor sums functions in almost all short intervals,” Integers, vol. 4, article A2, 9 pages, 2004. View at Google Scholar
  12. G. Coppola, “On the correlations, Selberg integral and symmetry of sieve functions in short intervals. II,” International Journal of Pure and Applied Mathematics, vol. 58, no. 3, pp. 281–298, 2010. View at Google Scholar
  13. G. Coppola and S. Salerno, “On the symmetry of the divisor function in almost all short intervals,” Acta Arithmetica, vol. 113, no. 2, pp. 189–201, 2004. View at Publisher · View at Google Scholar
  14. J. Kaczorowski and A. Perelli, “On the distribution of primes in short intervals,” Journal of the Mathematical Society of Japan, vol. 45, no. 3, pp. 447–458, 1993. View at Publisher · View at Google Scholar
  15. A. de Roton, “On the mean square of the error term for an extended Selberg class,” Acta Arithmetica, vol. 126, no. 1, pp. 27–55, 2007. View at Publisher · View at Google Scholar
  16. L. Fejér, “Über trigonometrische polynome,” Journal für die Reine und Angewandte Mathematik (Crelle's Journal), vol. 146, pp. 53–82, 1916. View at Google Scholar
  17. B. Green, “On arithmetic structures in dense sets of integers,” Duke Mathematical Journal, vol. 114, no. 2, pp. 215–238, 2002. View at Publisher · View at Google Scholar
  18. H. Iwaniec and E. Kowalski, Analytic Number Theory, vol. 53 of American Mathematical Society Colloquium Publications, American Mathematical Society, Providence, RI, USA, 2004.
  19. S. A. Amitsur, “Some results on arithmetic functions,” Journal of the Mathematical Society of Japan, vol. 11, pp. 275–290, 1959. View at Publisher · View at Google Scholar
  20. J. P. Tull, “Average order of arithmetic functions,” Illinois Journal of Mathematics, vol. 5, pp. 175–181, 1961. View at Google Scholar
  21. G. Coppola and M. Laporta, “A modified Gallagher’s Lemma,” http://arxiv.org/abs/1301.0008.