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ON MULTIPLICATIVE COMPOSITIONS OF INTEGERS

Part of: Multiplicative number theory Zeta and $L$-functions: analytic theory

Published online by Cambridge University Press:  29 November 2017

Hugh L. Montgomery  and
Gérald Tenenbaum
Hugh L. Montgomery
Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109–1043, U.S.A. email [email protected]
Gérald Tenenbaum
Affiliation:
Institut Élie Cartan, Faculté des Sciences, Université de Lorraine, B.P. 70239, 54506 Vandœuvre-lès-Nancy Cedex, France email [email protected]
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Abstract

We consider an arithmetic function defined independently by John G. Thompson and Greg Simay, with particular attention to its mean value, its maximal size, and the analytic nature of its Dirichlet series generating function.

MSC classification

Primary: 11N37: Asymptotic results on arithmetic functions 11N56: Rate of growth of arithmetic functions
Secondary: 11M41: Other Dirichlet series and zeta functions
Type
Research Article
Information
Mathematika , Volume 63 , Issue 3 , 2017 , pp. 1081 - 1090
Copyright
Copyright © University College London 2017 

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References

Freud, G., Restglied eines Tauberschen Satzes, I. Acta Math. Acad. Sci. Hungar. 2 1951, 299–308.Google Scholar
Ivić, A., The Riemann Zeta-Function. Theory and Applications, Dover Publications, Inc. (Mineola, NY, 2003). Reprint of the 1985 original, Wiley, New York.Google Scholar
Karamata, J., Review of Freud [ 1 ]. Zentalblatt für Math. 44 1952, 324.Google Scholar
Landau, E. and Walfisz, A., Über die Nichtfortsetzbarkeit einiger durch Dichichletsche Reihen definierte Funktionen. Rend. Circ. Mat. Palermo 44 1920, 82–86. Landau’s Collected Works, Vol. 7, Thales, Essen, 1986, 252–256.CrossRefGoogle Scholar
Montgomery, H. L. and Vaughan, R. C., Multiplicative Number Theory I: Classical Theory (Cambridge Studies in Advanced Mathematics 97 ), Cambridge University Press (Cambridge, 2007).Google Scholar
Salikhov, V. Kh., On the irrationality measure of ln3. Dokl. Akad. Nauk 417(6) 2007, 753–755 (Russian); Translation in Dokl. Math. 76(3) (2007), 955–957.Google Scholar
Tenenbaum, G., Introduction to Analytic and Probabilistic Number Theory (Graduate Studies in Mathematics 163 ), American Mathematical Society (Providence, RI, 2015).CrossRefGoogle Scholar
Wu, Q. and Wang, L., On the irrationality measure of log3. J. Number Theory 142 2014, 264–273.CrossRefGoogle Scholar