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Über gewisse Lambertsche Reihen, I: Verallgemeinerung der Modulfunktion η (τ) und ihrer Dedekindschen Transformationsformel

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Literatur

  1. Apostol, T. M.: Generalized Dedekind sums and transformation formulae of certain Lambert series. Duke Math. J.17, 147–157 (1950).

    Google Scholar 

  2. Carlitz, L.: Some theorems on generalized Dedekind sums. Pac. J. Math.3, 513–522 (1953).

    Google Scholar 

  3. Carlitz, L.: Dedekind sums and Lambert series. Proc. Amer. Math. Soc.5, 580–584 (1954).

    Google Scholar 

  4. Carlitz, L.: A further note on Dedekind sums. Duke Math. J.23, 219–223 (1956).

    Google Scholar 

  5. Dedekind, R.: Erläuterungen zu den Riemannschen Fragmenten über die Grenzfälle der elliptischen Funktionen. Ges. math. Werke1, Braunschweig 1930, 159–173.

    Google Scholar 

  6. Hardy, G. H., andS. Ramanujan: Asymptotic formulae in combinatory analysis. Proc. London Math. Soc. (2)17, 75–115 (1917).

    Google Scholar 

  7. Knopp, K.: Über Lambertsche Reihen. J. reine angew. Math.142, 283–315 (1913).

    Google Scholar 

  8. Knopp K.: Theorie und Anwendung der unendlichen Reihen, 4. Aufl. Berlin-Heidelberg 1947.

  9. Mikolás, M.: On certain sums generating the Dedekind sums and their reciprocity laws. Pac. J. Math. (im Erscheinen).

  10. Rademacher, H.: Zur Theorie der Modulfunktionen. J. reine angew. Math.167, 312–336 (1931).

    Google Scholar 

  11. Rademacher, H.: Generalization of the reciprocity formula for Dedekind sums. Duke Math. J.21, 391–397 (1954).

    Google Scholar 

  12. Rademacher, H.: On the transformation of log η (τ). J. Indian Math. Soc. (2)19, 25–30 (1955).

    Google Scholar 

  13. Rademacher, H., andA. Whiteman: Theorems on Dedekind sums. Amer. J. Math.63, 377–407 (1941).

    Google Scholar 

  14. Schoenfeld, L.: A transformation formula in the theory of partitions. Duke Math. J.11, 873–887 (1944).

    Google Scholar 

  15. Siegel, C. L.: A simple proof of\(\eta \left( {-- \frac{1}{\tau }} \right) = {\text{ }}\eta (\tau )\sqrt {\frac{\tau }{i}} \). Mathematika1, 4 (1954).

    Google Scholar 

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  1. Mathematisches Institut der Eötvös Loránd-Universität, Budapest

    Miklós Mikolás

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  1. Miklós Mikolás
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Mikolás, M. Über gewisse Lambertsche Reihen, I: Verallgemeinerung der Modulfunktion η (τ) und ihrer Dedekindschen Transformationsformel. Math Z 68, 100–110 (1957). https://doi.org/10.1007/BF01160334

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