Polylogarithms and arithmetic function spaces

Lutz Lucht; Anke Schmalmack

ArticleOriginal scientific text

Title

Polylogarithms and arithmetic function spaces

Authors ¹, ¹

Affiliations

Institut für Mathematik, Technische Universität Clausthal, Erzstraße 1, 38678 Clausthal-Zellerfeld, Germany

L. Bieberbach, Analytische Fortsetzung, Springer, Berlin, 1955.
A. Jonquière, Note sur le série $\sum \frac{x^{n}}{n^{s}}$ , Bull. Soc. Math. France 17 (1889), 142-152.
D. S. Kubert, The universal ordinary distribution, ibid. 107 (1979), 179-202.
L. Lewin, Structural Properties of Polylogarithms, Math. Surveys Monographs 37, Amer. Math. Soc., Providence, 1991.
L. G. Lucht, Power series with multiplicative coefficients, Math. Z. 177 (1981), 359-374.
L. G. Lucht and C. Methfessel, Recurrent sequences and affine functional equations, J. Number Theory 57 (1996), 105-113.
L. G. Lucht and F. Tuttas, Mean values of multiplicative functions and natural boundaries of power series with multiplicative coefficients, J. London Math. Soc. 19 (1979), 25-34.
J. Milnor, On polylogarithms, Hurwitz zeta functions, and the Kubert identities, Enseign. Math. 29 (1983), 281-322.
A. J. van der Poorten, Some facts that should be better known, especially about rational functions, in: Number Theory and Applications (Banff, 1988), R. A. Mollin (ed.), Kluwer, 1989, 497-528.
A. Schmalmack, Arithmetische Funktionen und holomorph fortsetzbare Potenzreihen, Dissertation, TU Clausthal, 1999.
W. Schwarz, Fourier-Ramanujan-Entwicklungen zahlentheoretischer Funktionen und Anwendungen, Festschrift Wiss. Ges. Univ. Frankfurt, Franz Steiner Verlag, Wiesbaden, 1981, 399-415.
W. Schwarz and J. Spilker, Arithmetical Functions, London Math. Soc. Lecture Note Ser. 184, Cambridge Univ. Press, Cambridge, 1994.
E. Seneta, Regularly Varying Functions, Lecture Notes in Math. 508, Springer, Berlin, 1976.

Title

Polylogarithms and arithmetic function spaces

Affiliations

Bibliography