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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some $ p$-adic versions of Polya's theorem on integer valued analytic functions


Authors: D. L. Hilliker and E. G. Straus
Journal: Proc. Amer. Math. Soc. 26 (1970), 395-400
MSC: Primary 10F45; Secondary 12B40
MathSciNet review: 0432560
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Abstract: It is shown that functions whose values at the positive integers lie in a fixed algebraic number field with exponential growth restrictions on the conjugates and common denominators of these values must be polynomials if they can be represented by functions which are analytic in sufficiently large disks of $ p$-adic planes.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0432560-X
PII: S 0002-9939(1970)0432560-X
Keywords: Algebraic number theory, integer valued analytic functions, analytic functions, $ p$-adic variable
Article copyright: © Copyright 1970 American Mathematical Society