Criteria for Algebraicity of Analytic Functions
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Abstract We consider functions defined on an open subset of a nonsingular, either real or complex, algebraic set. We give criteria for an analytic function to be a Nash (resp. regular, resp. polynomial) function. Our criteria depend only on the behavior of such a function along irreducible nonsingular algebraic curves passing through a given point. In the proofs we use results on algebraicity of formal power series, which are also established in this paper.
1984 ◽
Vol 4
(4)
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pp. 553-568
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1992 ◽
Vol 44
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pp. 194-205
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2003 ◽
Vol 184
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pp. 369-383
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2004 ◽
Vol 339
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pp. 533-538
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2002 ◽
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pp. 403-410
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2017 ◽
Vol 2018
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pp. 4780-4798
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2011 ◽
Vol 31
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pp. 331-343
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