Talk:Arithmetic function: Difference between revisions

Revision as of 23:52, 7 June 2017

Revision as of 08:16, 8 June 2017

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There are a few references in the article, e.g. "prime counting functions, which are not arithmetic functions", that imply that arithmetic function should have some precise definition. But the only definition I see of the term is "expresses some arithmetic property of n" which is not precise at all (at least without a link to arithmetic). Is it even a precise term, and if so, what is its definition? Can we make it clearer what the actual definition is? <!-- Template:Unsigned --><small class="autosigned">—&nbsp;Preceding [[Wikipedia:Signatures|unsigned]] comment added by [[User:Luqui|Luqui]] ([[User talk:Luqui#top|talk]] • [[Special:Contributions/Luqui|contribs]]) 23:50, 7 June 2017 (UTC)</small> <!--Autosigned by SineBot-->

: The apparently vague definition given by Hardy and Wright and mentioned in the first line of the article becomes clear in view of the classical functions they consider in their chapter 16. A more precise and less restrictive definition is however widely accepted by number theorists:

:"An arithmetic function is any real- or complex-valued function defined on the set N of positive integers. (In other words, an arithmetic function is just a sequence of real or complex numbers, though this point of view is not particularly useful)", see [http://www.math.illinois.edu/~ajh/ant/main1.pdf].[[User:Sapphorain|Sapphorain]] ([[User talk:Sapphorain|talk]]) 08:15, 8 June 2017 (UTC)