J. V. Leyendekkers and A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310–5132

Volume 11, 2005, Number 3, Pages 7–14

**Full paper (PDF, 161 Kb)**

## Details

### Authors and affiliations

J. V. Leyendekkers

*The University of Sydney, 2006 Australia*

A. G. Shannon

*Warrane College, Kensington, NSW 1465,
& KvB Institute of Technology, North Sydney, NSW 2060, Australia *

### Abstract

Thirteen convergent infinite series have been analysed in terms of modular rings. Thie enables one to assess the contribution of different categories of integers to the infinite series. One class of even integers contributes 1/6(*π*/4)^{2} to a zeta-function with exponent 2. Another class of even integers makes one quarter the contribution of all the integers to this series.

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## Cite this paper

Leyendekkers, J. V., and Shannon, A. G. (2005). Infinite series and modular rings. *Notes on Number Theory and Discrete Mathematics*, 11(3), 7-14.