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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 0136775
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References [Enhancements On Off] (What's this?)

  • [1] Richard Bellman, A brief introduction to theta functions, Athena Series: Selected Topics in Mathematics, Holt, Rinehart and Winston, New York, 1961. MR 0125252 (23 #A2556)
  • [2] Lars Gårding, The solution of Cauchy’s problem for two totally hyperbolic linear differential equations by means of Riesz integrals, Ann. of Math. (2) 48 (1947), 785–826. MR 0022648 (9,240a)
  • [3] Max Koecher, Über Thetareihen indefiniter quadratischer Formen, Math. Nachr. 9 (1953), 51–85 (German). MR 0067932 (16,801b)
  • [4] Hans Maass, Die Differentialgleichungen in der Theorie der Siegelschen Modulfunktionen, Math. Ann. 126 (1953), 44–68 (German). 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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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1961-0136775-4
PII: S 0002-9939(1961)0136775-4
Article copyright: © Copyright 1961 American Mathematical Society