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The reciprocity formula for multidimensional theta functions


Authors: Richard Bellman and R. Sherman Lehman
Journal: Proc. Amer. Math. Soc. 12 (1961), 954-961
MSC: Primary 33.19; Secondary 14.51
DOI: https://doi.org/10.1090/S0002-9939-1961-0136775-4
MathSciNet review: 0136775
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References [Enhancements On Off] (What's this?)

  • [1] R. Bellman, A brief introduction to theta functions, New York, Holt, Rinehart and Co., 1961. MR 0125252 (23:A2556)
  • [2] L.Gårding, The solution of Cauchy's problem for two totally hyperbolic linear differential equations by means of Riesz integrals, Ann. of Math. vol. 48 (1947) pp. 785-826. MR 0022648 (9:240a)
  • [3] M. Koecher, Ueber Thetareihen indefiniter quadratischer Formen, Math. Nachr. vol. 9 (1953) pp. 51-85. MR 0067932 (16:801b)
  • [4] H. Maass, Die Differentialgleichungen in der Theorie der Siegeischen Modulfunktionen, Math. Ann. vol. 126 (1953) pp. 44-68. MR 0065584 (16:449d)
  • [5] B. Riemann, Theorie der Abel'schen Funktionen in Collected works, pp. 88-144, New York, Dover Publications, Inc., 1953.

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DOI: https://doi.org/10.1090/S0002-9939-1961-0136775-4
Article copyright: © Copyright 1961 American Mathematical Society

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