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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
MathSciNet review: 1254837
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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.

References [Enhancements On Off] (What's this?)

  • [B] B. Berndt, Ramanujan's notebooks, Part III, Springer-Verlag, New York, Heidelberg, and Berlin, 1991. MR 1117903 (92j:01069)
  • [BB1] P. Borwein and J. Borwein, A cubic counterpart of Jacobi's Identity and the AGM, Trans. Amer. Math. Soc. 323 (1991), 691-701. MR 1010408 (91e:33012)
  • [BB2] -, $ \Pi $ and the AGM, Wiley, New York, 1987.
  • [FKO] H. Farkas and Yaacov Kopeliovich, New theta constant identities, Israel J. Math. 82 (1993), 133-141. MR 1239047 (94k:33044)
  • [FK] H. Farkas and I. Kra, Automorphic forms for subgroups of the modular group, Israel J. Math. 82 (1993), 87-132. MR 1239046 (94e:11040)
  • [M] D. Mumford, Tata lectures on Theta, Volume I, Birkhauser, Basel, 1983. MR 688651 (85h:14026)
  • [RF] H. E. Rauch and H. M. Farkas, Theta functions with applications to Riemann surfaces, Williams and Wilkins, Baltimore, MD, 1974. MR 0352108 (50:4595)

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Keywords: Theta identities
Article copyright: © Copyright 1995 American Mathematical Society

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