We analise periodic functions (mod r), keeping Cauchy multiplication as the basic tool, and pay particular attention to even functions (mod r) having the property f(n) = f((n,r)) for all n. We provide some new aspects into the Hilbert space structure of even functions (mod r) and make use of linera transformations to interpret the known number-theoretic formulae involving solutions of congruences.
@article{urn:eudml:doc:42426,
title = {Cauchy multiplication and periodic functions (mod r).},
journal = {Collectanea Mathematica},
volume = {42},
year = {1991},
pages = {33-44},
zbl = {0769.11001},
mrnumber = {MR1181060},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:42426}
}
Haukkanen, Pentti; Sivaramakrishnan, R. Cauchy multiplication and periodic functions (mod r).. Collectanea Mathematica, Tome 42 (1991) pp. 33-44. http://gdmltest.u-ga.fr/item/urn:eudml:doc:42426/