Pacific Journal of Mathematics

Utterly integer valued entire functions. I.

Daihachiro Sato

Article information

Source
Pacific J. Math., Volume 118, Number 2 (1985), 523-530.

Dates
First available in Project Euclid: 8 December 2004

Permanent link to this document
https://projecteuclid.org/euclid.pjm/1102706459

Mathematical Reviews number (MathSciNet)
MR789191

Zentralblatt MATH identifier
0575.30024

Subjects
Primary: 30D20: Entire functions, general theory

Citation

Sato, Daihachiro. Utterly integer valued entire functions. I. Pacific J. Math. 118 (1985), no. 2, 523--530. https://projecteuclid.org/euclid.pjm/1102706459


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References

  • [I] D. Brizolis and E. G. Straus,A basisfor the ring of doubly integer-valuedpolynomials, J. Reine Angew. Math., 286/287 (1976), 187-195.
  • [2] D. Brizolis, Ideals in rings of integer valuedpolynomials, J. Reine Angew. Math.,285 (1976), 28-52.
  • [3] L. Carlitz,A note on integral-valuedpolynomials, Nederl.Akad. Wetensch. Proc, Ser. A 62, Indag. Math., 21 (1959), 294-299.
  • [4] N. G. de Bruijn, Some classesof integer-valued functions, Nederl. Akad. Wetensch. Proc. Ser. A (58) (1955), 363-367.
  • [5] K. Rogers and E. G. Straus, Infinitely integer valued polynomials over an algebraic numberfield, Pacific J. Math., 118 (1985), 507-522.
  • [6] E. G. Straus, On thepolynomials whosederivatives have integral values at the integers, Amer. Math. Soc, 2 (1951), 24-27.
  • [7] E. G. Straus, Functionsperiodic modulo each of a sequence of integers, Duke Math. J., 19 (1952), 379-395. B. Integer Valued Functions, Completely Integer Valued Functions, Their Generalizations Without Derivative Conditions[8-27]
  • [8] R. C. Buck, A classof entirefunctions, Duke Math. J., 13 (1946), 541-559.
  • [9] R. C. Buck, Integral valuedentirefunctions, Duke Math. J., 15 (1948), 879-891.
  • [10] F. Carlson, ber ganzwertige Funktionen, Math. Z., 11 (1921), 1-23.
  • [II] S. Fukasawa, (Morimoto), Uberganzwertige ganze Funktionen, Tohoku Math. J., 27 (1926), 41-52.
  • [12] S. Fukasawa, Uberganzwertige ganze Funktionen, Tohoku Math. J., 29 (1928), 131-144.
  • [13] A. Gelfond, Sur un theoreme de M. G. Plya, Atti Acad. Naz. Lincei, Rend., classe di Scienze fisiche, mathematiche e naturali (6), 10 (1929), 569-574.
  • [14] G. H. Hardy, On a theorem of Mr. G. Pblya, Proc. Cambridge Phil. Soc, 19 (1920), 60-63.
  • [15] G. H. Hardy, On two theorems of F. Carlson and S. Wigert, Acta Math., 42 (1920), 327-339.
  • [16] D. L. Hilliker, On analytic functions which have algebraic values at a convergent sequence of points, Trans.Amer. Math. Soc, 126 (1967), 534-550.
  • [17] E. Landau, Note on Mr. Hardy's extension of a theorem of Mr. G. Pblya, Proc Cambridge Phil. Soc, 20 (1920), 14-15.
  • [18] C. Pisot, Uber ganzwertige ganze Funktionen, Jahrber. Deut. Math., 52 (1942), 95-102.
  • [19] C. Pisot, Sur les functions arithmetiques analytiques a croissance exponentielle, C. R. Acad. Sci. Paris,222 (1946), 988-990.
  • [20] C. Pisot, Sur les functions analytiques arithmetiques et presque arithmetiques, C. R. Acad. Sci. Paris,222 (1946), 1027-1028.
  • [21] G. Plya, Uberganzwertige ganze Funktionen, Rend. Circ Math. Palermo,40 (1915), 1-16.
  • [22] G. Plya, Uber Potenzreihen mit ganzzahligen Koeffizienten, Math. Ann., 77 (1916), 497-513.
  • [23] G. Plya, Uber ganzwertigeganze Funktionen, Nachr. Ges. Wiss. Gttingen, (1920), 1-10.
  • [24] Daihachiro Sato and E. G. Straus, Rate of growth of Hurwitz entire functions and integer valued entirefunctions, Bull. Amer. Math. Soc, 70 (1964), 303-307.
  • [25] A. Selberg, Uber ganzwertige ganze transzendente Funktionen, /, Arch. Math. Natur- vid., 44 (1941),45-52.
  • [26] A. Selberg, Uber ganzwertige ganze transzendente Funktionen II, Arch. Math. Naturvid., 44 (1941),171-181.
  • [27] E. G. Straus, On a class of integral-valued Dirichlet series, Proc. International Congress Math. I, (1950), 423. C. Integer Valued Functions With Finitely Many Integer Valued Derivatives[28-31].
  • [28] A. Gelfond, Sur les proprietes arithmetiques des functions entieres, Tohoku Math. J., 30 (1929),280-285.
  • [29] Th. Schneider, Bin Satz uber ganzwertige Funktionen als Prinzip fur Transzendenz- beweise, Math. Ann., 121 (1949),131-140.
  • [30] A. Selberg, Uber einen Satz von A. Gelfond, Arch. Math. Naturvid, 44 (1941), 159-170.
  • [31] C. L. Siegel, Uber einige Anwendungen diophantischer Approximationen, Abh. Preuss. Akad. Wiss., (1929),No.1. D. Hurwitz Functions and Generalizations in the One Point Case [32-35]
  • [32] S. Kakeya, Notes on the maximum modulus of afunction, Tohoku Math. J., 10(1916), 68-70.
  • [33] L. D. Neidleman and E. G. Straus, Functions whose derivatives at one point form a finite set, Trans. Amer. Math. Soc, 140 (1969),411-422.
  • [34] G. Plya, Uber die Kleinsten ganzen Funktionen deren smtliche Derivierte im Punkte z = 0 ganzzahligsind, Tohoku Math. J., 19 (1921),65-68.
  • [35] Daihachiro Sato and E. G. Straus, On the rate of growth of Hurwitz functions of a complex or p-adic variable, J. Math. Soc. of Japan, 17 (1965),17-29. E. Infinitely Integer Valued Functions With Finite Set of Interpolation [36-42]
  • [36] L. Bieberbach, Theorie der Geometrischen Konstruktionen, Lehrbcher und Mono- graphien aus dem Gebiete der Exakten Wissenschaften Bd 13, Verlag Birkh'auser Basel, (1952),126-138,159.
  • [37] L. Bieberbach, Uber einen Stz PblyscherArt, Arch. Math., 4 (1953),23-27.
  • [38] A. H. Cayford, A class of integer valued entire functions, Trans. Amer. Math. Soc, 141 (1969),415-432.
  • [39] P. Lockhart and E. G. Straus, Entire functions which are infinitely integer-valued at a fintie number of points, submittedto Trans. Amer. Math. Soc.
  • [40] Daihachiro Sato, On the type of highly integer valued entire functions, J. Reine Angew. Math., 248 (1971), 1-11.
  • [41] E. G. Straus, On entire functions with algebraic derivatives at certain algebraic points, Ann. Math., (2) 52 (1950),188-198.
  • [42] E. G. Straus, Some topics in integer valued functions, Report of the Institute of Number Theory, Boulder,Colorado, 1960, pp.99-103. F. Infinitely Integer Valued Functions With Unbounded Set of Interpolation [43-48].
  • [43] Daihachiro Sato, Integer Valued Entire Functions, Dissertation, Univ. of Calif., Los Angeles, June 1961.
  • [44] Daihachiro Sato, Two counter examples on integer valued entire functions, (Japanese), Sugaku, 14 (1962),95-98.
  • [45] Daihachiro Sato, A simple example of a transcendental entire function that together with all its derivatives assumes algebraic values at all algebraicpoints, Proc. Amer. Math. Soc, 14 (1963), 996.
  • [46] Daihachiro Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc, 69 (1963), 411-414.
  • [47] Daihachiro Sato and E. G. Straus, Generalized interpolation by analytic functions, Bull. Amer. Math. Soc, 72 (1966), 32-36.
  • [48] Daihachiro Sato and E. G. Straus, Generalized interpolation by analyticfunctions, J. Math. Sci. I, (1966), 53-76. G. Integer Valued Functions of Several Complex Variables [49-52].
  • [49] Alan Baker, A note on integral integer-valued functions of several variables, Proc. Cambridge Philos. Soc, 63 (1967), 715-720.
  • [50] Fred Gross, Integer valued entire functions of several complex variables, Dissertation, Univ. of Calif., Los Angeles, September 1962.
  • [51] Fred Gross, Entire functions all of whose derivatives are integral at the orign, Duke Math. J., 31 (1964), 617-622.
  • [52] Fred Gross, Entire functions of several variables with algebraic derivatives at certain algebraic points, Pacific J. Math., 31 (1969), 693-701. H. Integer Valued Functions of a/7-adic Variable [53-54]
  • [53] D. L. Hilliker, Algebraically dependent functions of a complex and p-adic variable, Proc Amer. Math. Soc, 19 (1968), 1052-1056.
  • [54] D. L. Hilliker and E. G. Straus, Some p-adic versions of Pblya's theorem on integer valued analytic functions, Proc. Amer. Math. Soc, 26, 3 (1970), 395-400. I. Differential Rings of Analytic Functions [55-57]
  • [55] E. G. Straus, Differential rings of meromorphic functions, Acta Arithmetica, 21 (1972), 271-284.
  • [56] E. G. Straus, (edited by C. F. Osgood), Differential rings of analytic functions of a non-Archimedean variable, in Diophantine Approximation and its Applications, Academic Press (1973), 295-308.
  • [57] A. H. Cayford and E. G. Straus, On differential rings of entire functions, Trans. Amer. Math. Soc, 209 (1975), 283-293. J. Related Topics [58-59]
  • [58] Daihachiro Sato, Note on the integer valued entire functions and transcendental numbers, (Japanese), Sugaku, 14 (1962), 99-108.
  • [59] Daihachiro Sato, On the rate of growth of rapidly increasing integral functions, (Japanese), Sugaku, 15 (1963), 101-105.