Hostname: page-component-848d4c4894-p2v8j Total loading time: 0 Render date: 2024-05-06T04:07:57.878Z Has data issue: false hasContentIssue false
  • English
  • Français

Evaluation of two convolution sums involving the sum of divisors function

Published online by Cambridge University Press:  17 April 2009

Mathieu Lemire  and
Kenneth S. Williams
Mathieu Lemire
Affiliation:
School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada, e-mail: mathieul@math.carleton.ca
Kenneth S. Williams
Affiliation:
Centre for Research in Algebra and Number Theory, School of Mathematics and Statistics, Carleton University, Ottawa, Ontario K1S 5B6, Canada, e-mail: williams@math.carleton.ca
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The convolution sums and are evaluated for all n ∈ ℕ.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 107 - 115
Copyright
Copyright © Australian Mathematical Society 2006

References

[1]Alaca, A., Alaca, S. and Williams, K.S., ‘The convolution sum ’ Canad. Math. Bull. (to appear).Google Scholar
[2]Alaca, S. and Williams, K.S., ‘The convolution sums and ’, (submitted).Google Scholar
[3]Berndt, B.C., Chan, H.H., Sohn, J. and Son, S.H., ‘Eisenstein series in Ramanujan's lost notebook’, Ramanujan J. 4 (2000), 81–114.CrossRefGoogle Scholar
[4]Besge, M., ‘Extrait d'une lettre de M. Besge à M. Liouville’, J. Math. Pures Appl. 7 (1862), 256.Google Scholar
[5]Glaisher, J.W.L., ‘On the square of the series in which the coefficients are the sums of the divisors of the exponents’, Mess. Math. 14 (1885), 156–163.Google Scholar
[6]Glaisher, J.W.L., Mathematical Papers 1883–1885 (Cambridge, 1885).Google Scholar
[7]Huard, J.G., Ou, Z.M., Spearman, B.K. and Williams, K.S., ‘Elementary evaluation of certain convolution sums involving divisor functions’, in Number Theory for the Millenium II (A.K. Peters, Natick, MA, 2002), pp. 229–274.Google Scholar
[8]Melfi, G., Some problems in elementary number theory and modular forms, Ph.D thesis (University of Pisa, 1998).Google Scholar
[9]Melfi, G., ‘On some modular identities’, in Number Theory (de Gruyter, Berlin, 1998). pp. 371–382.Google Scholar
[10]Williams, K.S., ‘A cubic transformation formula for and some arithmetic convolution formulae’, Math. Proc. Cambridge Philos. Soc. 137 (2004), 519–539.Google Scholar
[11]Williams, K.S., ‘The convolution sum ’, Pacific J. Math. (to appear).Google Scholar
[12]Williams, K.S., ‘The convolution sum ’, Int. J. Number Theory 1 (2005), 193–205.Google Scholar