Abstract
A new simple proof of the transformation formula for the Dedekind eta-function is given. Some connections with certain infinite series are made.
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References
T. M. Apostol, Modular Functions and Dirichlet Series in Number Theory,Springer-Verlag, New York, 1976.
B. C. Berndt, Generalized Dedekind eta-functions and generalized Dedekind sums, Trans. Amer. Math. Soc. 178 (1973), 495–508
B. C. Berndt, Modular transformations and generalizations of several formulae of Ramanujan, Rocky Mt. J. Math. 7 (1977), 147–189.
B. C. Berndt, Ramanujan’s Notebooks, Part II, Springer-Verlag, New York, 1989.
B. C. Berndt, Ramanujan’s Notebooks, Part III, Springer-Verlag, New York, 1991.
K. Kiyek and H Schmidt, Auswertung einiger spezieller unendlicher Reihen aus dem Bereich der elliptischen Funktionen, Arch. Math. 18 (1967), 438–443.
M. I. Knopp, Modular Functions in Analytic Number Theory,Chelsea, New York, 1993.
J. Lagrange, Une formule sommatoire et ses applications, Bull. Sci. Math. (2) 84 (1960), 105–110.
C.-B. Ling, On summation of series of hyperbolic functions, SIAM J. Math. Anal. 6 (1975), 551–562.
B. Muckenhoupt, The norm of a discrete singular transform, Studia Math. 25 (1964/65), 97–102.
T. S. Nanjundiah, Certain summations due to Ramanujan, and their generalisations, Proc. Indian Acad. Sci.,Sect. A 34 (1951), 215–228.
S. Ramanujan, Notebooks (2 volumes), Tata Institute of Fundamental Research, Bom-bay, 1957.
R. E. Shafer, Problem 5063, with solutions by A. E Livingston and J. Raleigh, Amer. Math. Monthly 70 (1963), 1110–1111.
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© 2001 Kluwer Academic Publishers
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Berndt, B.C., Venkatachaliengar, K. (2001). On the Transformation Formula for the Dedekind Eta-Function. In: Garvan, F.G., Ismail, M.E.H. (eds) Symbolic Computation, Number Theory, Special Functions, Physics and Combinatorics. Developments in Mathematics, vol 4. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0257-5_5
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DOI: https://doi.org/10.1007/978-1-4613-0257-5_5
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