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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0432560-X
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 $p$-adic planes.
- 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 204365, DOI https://doi.org/10.1090/S0002-9947-1967-0204365-0
- D. L. Hilliker, Algebraically dependent functions of a complex and $p$-adic variable, Proc. Amer. Math. Soc. 19 (1968), 1052–1056. MR 231807, DOI https://doi.org/10.1090/S0002-9939-1968-0231807-3 G. Pólya, Über ganzwertige ganze Funktionen, Rend Circ. Mat. Palermo 40 (1915), 1-16.
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Keywords:
Algebraic number theory,
integer valued analytic functions,
analytic functions,
<IMG WIDTH="16" HEIGHT="37" ALIGN="MIDDLE" BORDER="0" SRC="images/img2.gif" ALT="$p$">-adic variable
Article copyright:
© Copyright 1970
American Mathematical Society