On the rate of growth of Hurwitz functions of a complex or p-adic variable

Daihachiro SATO; Ernst G. STRAUS

doi:10.2969/jmsj/01710017

Daihachiro SATO, Ernst G. STRAUS

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1965 Volume 17 Issue 1 Pages 17-29

DOI https://doi.org/10.2969/jmsj/01710017

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Published: 1965 Received: November 12, 1962 Available on J-STAGE: September 26, 2006 Accepted: - Advance online publication: - Revised: -
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Date of correction: September 26, 2006 Reason for correction: - Correction: CITATION Details: Wrong : 1) S. Kakeya, Notes on the maximum modulus of a function, Tohoku Math. J., 10 (1916), 68-70.
2) G. Polya, Uber die kleinsten ganzen Funktionen deren samtliche Derivierte im Punkte z=0 ganzzahlig sind, Tohoku Math. J., 19 (1921), 65-68.
3) D. Sato, Integer valued entire functions, Dissertation, Univ. of Calif., Los Angeles, June, 1961.
4) E. G. Straus, On entire functions with algebraic derivatives at certain algebraic points, Ann. Math., 52 (1950), 188-198.
5) L. Bieberbach, Theorie der Geometrischen Konstruktionen, Lehrbücher und Monographen aus dem Gebiete der Exakten Wissenschaften Bd. 13, Verlag Birkhäuser Basel, (1952), 126-138, 159.
6) L. Bieberbach, Über einen Satz Polyascher Art, Arch. Math., 4 (1953), 23-27.
7) A. H. Cayford, A class of integer valued entire functions, Dissertation, Univ. of Calif., Los Angeles, June, 1961.
8) D. Sato, Two counter examples on integer valued entire functions (Japanese), Sugaku, 14 (1962), 95-98.
9) D. Sato, Note on the integer valued entire functions and transcendental numbers (Japanese), Sugaku, 14 (1962), 99-108.
10) E. G. Straus, Some topics in integer valued functions, Report of the institute of number theory, Boulder Colorado, (1960), 99-103.
11) C. Pisot, Quelques aspects de la theorie des entiers algébriques, Seminaire de Mathématiques Supérieures, Université de Montréal.
12) B. Dwork, On the rationality of the zeta function of an algebraic variety, Amer. J. Math., 82 (1960), 631-648.
13) D. Sato, A simple example of a transcendental entire function that together with all its derivatives assumes algebraic values at all algebraic points, Proc. Amer. Math. Soc., 14, 16 (1963), 996.
14) D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69, (1963), 411-414.
15) F. Gross, Integer valued entire functions of several complex variables, Dissertation, Univ. of Calif., Los Angeles, Sept., 1962.
16) D. Sato and E. G. Straus, A generalized interpolation by analytic functions, (to appear).

Right : [1] S. Kakeya, Notes on the maximum modulus of a function, Tôhoku Math. J., 10 (1916), 68-70.
[2] G. Pólya, Über die kleinsten ganzen Funktionen deren sämtliche Derivierte im Punkte z=0 ganzzahlig sind, Tôhoku Math. J., 19 (1921), 65-68.
[3] D. Sato, Integer valued entire functions, Dissertation, Univ. of Calif., Los Angeles, June, 1961.
[4] E. G. Straus, On entire functions with algebraic derivatives at certain algebraic points, Ann. Math., 52 (1950), 188-198.
[5] L. Bieberbach, Theorie der Geometrischen Konstruktionen, Lehrbücher und Monographen aus dem Gebiete der Exakten Wissenschaften Bd. 13, Verlag Birkhäuser Basel, (1952), 126-138, 159.
[6] L. Bieberbach, Über einen Satz Pólyascher Art, Arch. Math., 4 (1953), 23-27.
[7] A. H. Cayford, A class of integer valued entire functions, Dissertation, Univ. of Calif., Los Angeles, June, 1961.
[8] D. Sato, Two counter examples on integer valued entire functions (Japanese), Sugaku, 14 (1962), 95-98.
[9] D. Sato, Note on the integer valued entire functions and transcendental numbers (Japanese), Sugaku, 14 (1962), 99-108.
[10] E. G. Straus, Some topics in integer valued functions, Report of the institute of number theory, Boulder Colorado, (1960), 99-103.
[11] C. Pisot, Quelques aspects de la theorie des entiers algébriques, Seminaire de Mathématiques Supérieures, Université de Montréal.
[12] B. Dwork, On the rationality of the zeta function of an algebraic variety, Amer. J. Math., 82 (1960), 631-648.
[13] D. Sato, A simple example of a transcendental entire function that together with all its derivatives assumes algebraic values at all algebraic points, Proc. Amer. Math. Soc., 14, 16 (1963), 996.
[14] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69, (1963), 411-414.
[15] F. Gross, Integer valued entire functions of several complex variables, Dissertation, Univ. of Calif., Los Angeles, Sept., 1962.
[16] D. Sato and E. G. Straus, A generalized interpolation by analytic functions, (to appear).

Date of correction: September 26, 2006 Reason for correction: - Correction: PDF FILE Details: -

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