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Algebraic Approaches to Periodic Arithmetical Maps

✍ Scribed by Zhi-Wei Sun

Publisher: Elsevier Science
Year: 2001
Tongue: English
Weight: 170 KB
Volume: 240
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8721

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✦ Synopsis

A residue class a + n with weight λ is denoted by λ a n . For a finite system = λ s a s n s k s=1 of such triples, the periodic map w x = n s x-a s λ s is called the covering map of . Some interesting identities for those with a fixed covering map have been known; in this paper we mainly determine all those functions f → such that k s=1 λ s f a s + n s depends only on w where 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 s=1 λ s e 2πia s x/n s and ω x = 1 ≤ s ≤ k x + a s n s = 1 .

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