×

Über gewisse Lambertsche Reihen. I: Verallgemeinerung der Modulfunktion \(\eta(\tau)\) und ihrer Dedekindschen Transformationsformel. (German) Zbl 0078.07003


PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[1] Apostol, T. M.: Generalized Dedekind sums and transformation formulae of certain Lambert series. Duke Math. J.17, 147-157 (1950). · Zbl 0039.03801
[2] Carlitz, L.: Some theorems on generalized Dedekind sums. Pac. J. Math.3, 513-522 (1953). · Zbl 0057.03701
[3] Carlitz, L.: Dedekind sums and Lambert series. Proc. Amer. Math. Soc.5, 580-584 (1954). · Zbl 0057.03702
[4] Carlitz, L.: A further note on Dedekind sums. Duke Math. J.23, 219-223 (1956). · Zbl 0074.03504
[5] Dedekind, R.: Erläuterungen zu den Riemannschen Fragmenten über die Grenzfälle der elliptischen Funktionen. Ges. math. Werke1, Braunschweig 1930, 159-173.
[6] Hardy, G. H., andS. Ramanujan: Asymptotic formulae in combinatory analysis. Proc. London Math. Soc. (2)17, 75-115 (1917). · JFM 46.0198.04
[7] Knopp, K.: Über Lambertsche Reihen. J. reine angew. Math.142, 283-315 (1913). · JFM 44.0290.04
[8] Knopp K.: Theorie und Anwendung der unendlichen Reihen, 4. Aufl. Berlin-Heidelberg 1947. · Zbl 0031.11801
[9] Mikolás, M.: On certain sums generating the Dedekind sums and their reciprocity laws. Pac. J. Math. (im Erscheinen). · Zbl 0081.04302
[10] Rademacher, H.: Zur Theorie der Modulfunktionen. J. reine angew. Math.167, 312-336 (1931). · Zbl 0003.21501
[11] Rademacher, H.: Generalization of the reciprocity formula for Dedekind sums. Duke Math. J.21, 391-397 (1954). · Zbl 0057.03801
[12] Rademacher, H.: On the transformation of log ? (?). J. Indian Math. Soc. (2)19, 25-30 (1955). · Zbl 0064.32703
[13] Rademacher, H., andA. Whiteman: Theorems on Dedekind sums. Amer. J. Math.63, 377-407 (1941). · Zbl 0025.02802
[14] Schoenfeld, L.: A transformation formula in the theory of partitions. Duke Math. J.11, 873-887 (1944). · Zbl 0060.10104
[15] Siegel, C. L.: A simple proof of \(\eta \left( {-- \frac{1}{\tau }} \right) = {\text{ }}\eta (\tau )\sqrt {\frac{\tau }{i}} \) . Mathematika1, 4 (1954). · Zbl 0056.29504
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.