On the additive formulae of the theta functions and a collection of Lambert series pertaining to the modular equations of degree $5$
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- by Li-Chien Shen PDF
- Trans. Amer. Math. Soc. 345 (1994), 323-345 Request permission
Abstract:
We examine the connection between the additive formulae of the theta functions, the Fourier series expansion of the 12 elliptic functions, and the logarithmic derivatives of the theta functions. As an application, we study the Lambert series related to the modular equations of degree 5 and many interesting identities of Ramanujan are found in this process.References
- Bruce C. Berndt, Ramanujan’s notebooks. Part III, Springer-Verlag, New York, 1991. MR 1117903, DOI 10.1007/978-1-4612-0965-2
- John D. Fay, Theta functions on Riemann surfaces, Lecture Notes in Mathematics, Vol. 352, Springer-Verlag, Berlin-New York, 1973. MR 0335789 S.A. McCullough, Nevanlinna-Pick interpolation and canonical mapping functions, preprint.
- Scott McCullough and Li-Chien Shen, On the Szegő kernel of an annulus, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1111–1121. MR 1189748, DOI 10.1090/S0002-9939-1994-1189748-9 E.T. Whittaker and G.N. Watson, Modern analysis, 4th ed., Cambridge Univ. Press, London and New York, 1958.
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 345 (1994), 323-345
- MSC: Primary 33D10; Secondary 11F27
- DOI: https://doi.org/10.1090/S0002-9947-1994-1250827-3
- MathSciNet review: 1250827