Infinite series and modular rings

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.

References

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