Journal of the Ramanujan Mathematical Society

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Integer Valued Functions on Products


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1 Universite P.ET M. Crie (Paris VI), Institut Mathematique De Jussieu, Problems Diophantiens, Case 2474, Place Jussieu F-75252 Paris Cedex 05, France
     

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Let X and Y be two infinite subsets of C and ∫ an entire function such that f(xy) ∈ Z for any x ∈ X and y ∈ Y. Assuming some growth conditions on/ (upper bound) and on the size of X and Y (lower*, bounds), we deduce that/must be a polynomial.
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  • Integer Valued Functions on Products

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Authors

Michel Waldschmidt
Universite P.ET M. Crie (Paris VI), Institut Mathematique De Jussieu, Problems Diophantiens, Case 2474, Place Jussieu F-75252 Paris Cedex 05, France

Abstract


Let X and Y be two infinite subsets of C and ∫ an entire function such that f(xy) ∈ Z for any x ∈ X and y ∈ Y. Assuming some growth conditions on/ (upper bound) and on the size of X and Y (lower*, bounds), we deduce that/must be a polynomial.