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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  of it has zeros for suitable  's.
- [1]
Lu
Qi-keng, On Kaehler manifolds with constant curvature, Chinese
Math.–Acta 8 (1966), 283–298. 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
0239066 (39 #425), http://dx.doi.org/10.1090/S0002-9939-1969-0239066-3
- [3]
Menahem
Schiffer, The kernel function of an orthonormal system, Duke
Math. J. 13 (1946), 529–540. MR 0019115
(8,371a)
- [4]
M.
Skwarczyński, The invariant distance in the theory
of pseudoconformal transformations and the Lu Qi-keng conjecture,
Proc. Amer. Math. Soc. 22 (1969), 305–310. MR 0244512
(39 #5826), http://dx.doi.org/10.1090/S0002-9939-1969-0244512-5
- [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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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1976-0425185-9
PII:
S 0002-9939(1976)0425185-9
Keywords:
Kernel function,
Bergman kernel,
Riemann surface
Article copyright:
© Copyright 1976 American Mathematical Society
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