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On generalised Möbius inversion formulas

Published online by Cambridge University Press:  17 April 2009

Tian-Xiao He ,
Leetsch C. Hsu  and
Peter J.S. Shiue
Tian-Xiao He
Affiliation:
Department of Mathematics and Computer Science, Illinois Wesleyan University, Bloomington, IL 61702–2900, United States of America
Leetsch C. Hsu
Affiliation:
Department of Mathematical Sciences, University of Nevada, Las Vegas, Las Vegas, NV 89154–4020, United States of America
Peter J.S. Shiue
Affiliation:
Department of Mathematics, Dalian University of Technology, Dalian 116024, People's Republic of China
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We provide a wide class of Möbius inversion formulas in terms of the generalised Möbius functions and their application to the setting of the Selberg multiplicative functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 73 , Issue 1 , February 2006 , pp. 79 - 88
Copyright
Copyright © Australian Mathematical Society 2006

References

Referenes

[1]Brown, T.C., Hsu, L.C., Wang, J. and Shiue, P.J.S., ‘On a certain kind of generalized number-theoretical Möbius function’, Math. Sci. 25 (2000), 72–77.Google Scholar
[2]Bundschuh, P., Hsu, L.C. and Shiue, P.J.S., ‘Generalized Möbius inversion- theoretical and computational aspects’, (manuscript) (2003).Google Scholar
[3]Chen, N.-X., ‘Modified Möbius inversion formula and its application to physics’, Phys. Rev. Lett. 64 (1990), 1193–1195.CrossRefGoogle Scholar
[4]Fleck, A., ‘Über gewisse allgemeine zahlentheoretische Funktionen, insbesondere eine der Funktion μ(n) verwandte Funktion μk(m)’, S.-B. Berlin. Math. Ges 15 (1916), 3–8.Google Scholar
[5]Hardy, G.H. and Wright, E.M., An Introduction to the Theory of Numbers, (fifth edition) (Oxford University Press, New York, 1979).Google Scholar
[6]Knopfmacher, J., Abstract analytic number theory (North-Holland Publishing Co., Amsterdam, 1975).Google Scholar
[7]Sándor, J. and Bege, A., ‘The Möbius function: generalizations and extensions’, Adv. Stud. Contemp. Math. (Kyungshang) 6 (2003), 77–128.Google Scholar
[8]Selberg, A., ‘Remarks on multiplicative functions in: Number theory day’,(Proc. Conf., Rockfeller Univ.,New York), Lecture Notes in Mathematics 626 (Springer-Verlag, Berlin), pp. 232–241.Google Scholar
[9]Wilf, H.S., Generatingfunctionology (Academic Press, New York, 1990).Google Scholar