Some -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 | References | Similar Articles | Additional Information

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 -adic planes.

**[1]**D. L. Hilliker,*On analytic functions which have algebraic values at a convergent sequence of points*, Trans. Amer. Math. Soc.**126**(1967), 534–550. MR**0204365**, 10.1090/S0002-9947-1967-0204365-0**[2]**D. L. Hilliker,*Algebraically dependent functions of a complex and 𝑝-adic variable.*, Proc. Amer. Math. Soc.**19**(1968), 1052–1056. MR**0231807**, 10.1090/S0002-9939-1968-0231807-3**[3]**G. Pólya,*Über ganzwertige ganze Funktionen*, Rend Circ. Mat. Palermo**40**(1915), 1-16.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0002-9939-1970-0432560-X

Keywords:
Algebraic number theory,
integer valued analytic functions,
analytic functions,
-adic variable

Article copyright:
© Copyright 1970
American Mathematical Society