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An undecidable property of definite integrals

Author(s): Daniel T. Stallworth; Fred W. Roush
Journal: Proc. Amer. Math. Soc. 125 (1997), 2147-2148.
MSC (1991): Primary 03B25
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Abstract: We show that it is undecidable whether the definite contour multiple integral of an elementary meromorphic function is zero over an everywhere real analytic manifold on which it is analytic.

References:

[A]: A. Adler, Some recursively unsolvable problems in analysis, Proc. Amer. Math. Soc. 22 (1969), 523-526. MR 40:1277
[DL]: J. Denef and L. Lipschitz, Decision problems for differential equations, J. Symbolic Logic 54 (1989), 941-949. MR 91b:03074
[R]: D. Richardson, Some undecidable problems involving elementary functions of a real variable, J. Symbolic Logic 33 (1968), 514-520. MR 39:1330


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