Arithmetic function: Difference between revisions

Revision as of 13:23, 27 February 2007

Revision as of 13:27, 27 February 2007

Line 1:

In [[number theory]] and [[computability theory]], subfields of [[mathematics]], a '''number-theoretic function''' is any [[function (mathematics)|function]] whose ___domain is the set of [[natural number]]s.<ref>{{cite book

<ref>{{cite book

|title=Introduction to Mathematical Logic

|author=Elliott Mendelson

|year=1987

|publisher=CRC Press

|isbn 0412808307}}<br/>

{{cite book

|title=Fundamentals of Number Theory

|author=William J. LeVeque

|year=1996

|publisher=Courier Dover Publications

|isbn=0486689069}}<br/ref>

<ref>{{cite book

|title=Introduction to Mathematical Logic

|author=Elliott Mendelson

|year=1987

|publisher=CRC Press

|isbn =0412808307}}<br/ref>

A number-theoretic function whose range is included in the set of [[complex number]]s is called an '''arithmetical function'''.<ref>

Line 19 ⟶ 18:

|year=1974

|publisher=Intext Educational Publishers

|isbn =0700224564}}<br/>

{{cite book

|title=Classical Theory of Arithmetic Functions

|firstauthorauthor=R. Sivaramakrishnan and Sivaramakrishnan Sivaramakrishnan

|yaryear=1988

|secondauthor=Sivaramakrishnan Sivaramakrishnan

|yar=1988

|publisher=Marcel Dekker

|isbn= 0824780817}}</ref>

Line 45 ⟶ 43:

* Λ(''n''), the [[von Mangoldt function]] which is defined to be ln(''p'') if ''n'' is an integer power of a prime ''p'' and 0 for all other ''n''.

==Footnotes==

<references/>

[[Category:Arithmetic functions|*]]