New theta constant identities. II
Authors:
Hershel M. Farkas and Yaacov Kopeliovich
Journal:
Proc. Amer. Math. Soc. 123 (1995), 1009-1020
MSC:
Primary 11F27; Secondary 33E05
DOI:
https://doi.org/10.1090/S0002-9939-1995-1254837-8
MathSciNet review:
1254837
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Abstract | References | Similar Articles | Additional Information
Abstract: We apply the residue theorem to prove some of Ramanujan’s identities and modular equations. Some of the identities already appeared in Israel J. Math. (82 (1993), 133-141), but the proofs are given in this note.
- Bruce C. Berndt, Ramanujan’s notebooks. Part III, Springer-Verlag, New York, 1991. MR 1117903
- J. M. Borwein and P. B. Borwein, A cubic counterpart of Jacobi’s identity and the AGM, Trans. Amer. Math. Soc. 323 (1991), no. 2, 691–701. MR 1010408, DOI https://doi.org/10.1090/S0002-9947-1991-1010408-0 ---, $\Pi$ and the AGM, Wiley, New York, 1987.
- Hershel M. Farkas and Yaacov Kopeliovich, New theta constant identities, Israel J. Math. 82 (1993), no. 1-3, 133–140. MR 1239047, DOI https://doi.org/10.1007/BF02808110
- Hershel M. Farkas and Irwin Kra, Automorphic forms for subgroups of the modular group, Israel J. Math. 82 (1993), no. 1-3, 87–131. MR 1239046, DOI https://doi.org/10.1007/BF02808109
- David Mumford, Tata lectures on theta. I, Progress in Mathematics, vol. 28, Birkhäuser Boston, Inc., Boston, MA, 1983. With the assistance of C. Musili, M. Nori, E. Previato and M. Stillman. MR 688651
- Harry E. Rauch and Hershel M. Farkas, Theta functions with applications to Riemann surfaces, The Williams & Wilkins Co., Baltimore, Md., 1974. MR 0352108
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Keywords:
Theta identities
Article copyright:
© Copyright 1995
American Mathematical Society
