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Multiplicative function
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==References== * See chapter 2 of {{Apostol IANT}} * P. J. McCarthy, Introduction to Arithmetical Functions, Universitext. New York: Springer-Verlag, 1986. * {{cite journal |title=Efficient estimation of a multivariate multiplicative volatility model |journal=Journal of Econometrics |date=2010 |volume=159 |issue=1 |pages=55–73 |doi=10.1016/j.jeconom.2010.04.007 |s2cid=54812323 |url=http://sticerd.lse.ac.uk/dps/em/em541.pdf |last1=Hafner |first1=Christian M. |last2=Linton |first2=Oliver }} *{{cite journal |author=P. Haukkanen |title=Some characterizations of specially multiplicative functions |journal=Int. J. Math. Math. Sci. |volume=2003 |pages=2335–2344 |year=2003 |issue=37 |doi=10.1155/S0161171203301139 |doi-access=free |url=https://www.emis.de/journals/HOA/IJMMS/Volume2003_37/515979.abs.html }} *{{cite journal |author=P. Haukkanen |title=Extensions of the class of multiplicative functions |journal=East–West Journal of Mathematics |volume=14 |issue=2 |pages=101–113 |year=2012 |url=http://eastwestmath.org/index.php/ewm/article/view/100/98 }} *{{cite journal |author=DB Lahiri |title=Hypo-multiplicative number-theoretic functions |journal=Aequationes Mathematicae |volume=8 |issue=3 |pages=316–317 |year=1972 |doi=10.1007/BF01844515 }} *{{cite journal |author=D. Rearick |title=Semi-multiplicative functions |journal=Duke Math. J. |volume=33 |pages=49–53 |year=1966}} *{{cite journal |author=L. Tóth |title=Two generalizations of the Busche-Ramanujan identities |journal=International Journal of Number Theory |volume=9 |pages=1301–1311 |year=2013 |issue=5 |doi=10.1142/S1793042113500280 |arxiv=1301.3331 }} *{{cite journal |author=R. Vaidyanathaswamy |author-link=Ramaswamy S. Vaidyanathaswamy |title=The theory of multiplicative arithmetic functions |journal=Transactions of the American Mathematical Society |volume=33 |issue=2 |pages=579–662 |year=1931 |doi=10.1090/S0002-9947-1931-1501607-1 |doi-access=free }} *S. Ramanujan, Some formulae in the analytic theory of numbers. Messenger 45 (1915), 81--84. *E. Busche, Lösung einer Aufgabe über Teileranzahlen. Mitt. Math. Ges. Hamb. 4, 229--237 (1906) *A. Selberg: Remarks on multiplicative functions. Number theory day (Proc. Conf., Rockefeller Univ., New York, 1976), pp. 232–241, Springer, 1977.
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