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## ALGEBRAIC APPROACHES TO PERIODIC ARITHMETICAL MAPS

### Abstract

A residue class a + nZ with weight λ is denoted by 〈λ, a, n〉. For a finite system A = {〈λs, as, ns〉} k s=1 of such triples, the periodic map wA(x) = ∑ ns|x−as λs is called the covering map of A. Some interesting identities for those A with a fixed covering map have been known, in this paper we mainly determine out all those functions f: Ω → C such that ∑k s=1 λsf(as + nsZ) depends only on wA where Ω denotes the family of all residue classes. We also study algebraic structures related to such maps f, and periods of arithmetical functions ψ(x) = ∑k 2πiasx/ns s=1 λse and ω(x) = |{1 � s � k: (x + as, ns) = 1}|

Year: 2001
OAI identifier: oai:CiteSeerX.psu:10.1.1.189.3665
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