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Proceedings of the American Mathematical Society

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On the Lu Qi-keng conjecture

Authors: Nobuyuki Suita and Akira Yamada
Journal: Proc. Amer. Math. Soc. 59 (1976), 222-224
MSC: Primary 32H10; Secondary 30A31
MathSciNet review: 0425185
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Abstract: We shall give a complete answer to the Lu Qi-keng conjecture for finite Riemann surfaces. Our result is that every finite Riemann surface which is not simply-connected is never a Lu Qi-keng domain, i.e. the Bergman kernel $ K(z,t)$ of it has zeros for suitable $ t$'s.

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

  • [1] Lu Qi-keng, On Kaehler manifolds with constant curvature, Acta Math. Sinica 16 (1966), 269-281 = Chinese Math.-Acta 8 (1966), 283-298. MR 34 #6806. MR 0206990 (34:6806)
  • [2] Paul Rosenthal, On the zeros of the Bergman function in doubly-connected domains, Proc. Amer. Math. Soc. 21 (1969), 33-35. MR 39 #425. MR 0239066 (39:425)
  • [3] M. Schiffer, The kernel function of an orthonormal system, Duke Math. J. 13 (1946), 529-540. MR 8, 371. MR 0019115 (8:371a)
  • [4] M. Skwarczynski, The invariant distance in the theory of pseudoconformal transformations and the Lu Qi-keng conjecture, Proc. Amer. Math. Soc. 22 (1969), 305-310. MR 39 #5826. MR 0244512 (39:5826)

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Keywords: Kernel function, Bergman kernel, Riemann surface
Article copyright: © Copyright 1976 American Mathematical Society

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