The error term in Nevanlinna theory. (English) Zbl 0659.32005
In the 60th, the author conjectured that the Roth’s theorem could be improved of an inequality of some type of order \(1+\epsilon\) of log q. He deals here with the Stoll-Carlson-Griffiths theorem in higher dimensions and discusses the error term.
Reviewer: J.Kajiwara
MSC:
| 32A22 | Nevanlinna theory; growth estimates; other inequalities of several complex variables |
References:
| [1] | W. Adams, Asymptotic Diophantine approximations to \(e\) , Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 28-31. JSTOR: · Zbl 0131.04704 · doi:10.1073/pnas.55.1.28 |
| [2] | W. Adams, Asymptotic diophantine approximations and Hurwitz numbers , Amer. J. Math. 89 (1967), 1083-1108. JSTOR: · Zbl 0189.05001 · doi:10.2307/2373420 |
| [3] | J Carlson and P. Griffiths, A defect relation for equidimensional holomorphic mappings between algebraic varieties , Ann. of Math. (2) 95 (1972), 557-584. JSTOR: · Zbl 0248.32018 · doi:10.2307/1970871 |
| [4] | Shiing-shen Chern, Complex analytic mappings of Riemann surfaces. I , Amer. J. Math. 82 (1960), 323-337. JSTOR: · Zbl 0103.30104 · doi:10.2307/2372738 |
| [5] | P. A. Griffiths, Entire holomorphic mappings in one and several complex variables , Princeton University Press, Princeton, N. J., 1976. · Zbl 0317.32023 |
| [6] | S. Lang, Asymptotic Diophantine approximations , Proc. Nat. Acad. Sci. U.S.A. 55 (1966), 31-34. · Zbl 0135.10801 · doi:10.1073/pnas.55.1.31 |
| [7] | S. Lang, Differential manifolds , Springer-Verlag, New York, 1985, (Reprint from Addison-Wesley, Reading, MA, 1972). · Zbl 0551.58001 |
| [8] | S. Lang, Higher dimensional diophantine problems , Bull. Amer. Math. Soc. 80 (1974), 779-787. · Zbl 0298.14014 · doi:10.1090/S0002-9904-1974-13516-0 |
| [9] | S. Lang, Introduction to diophantine approximations , Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966. · Zbl 0144.04005 |
| [10] | S. Lang, Real analysis , Addison-Wesley Publishing Company Advanced Book Program, Reading, MA, 1983. · Zbl 0502.46003 |
| [11] | S. Lang, Report on diophantine approximations , Bull. Soc. Math. France 93 (1965), 177-192. · Zbl 0135.10802 |
| [12] | R. Nevanlinna, Analytic functions , Translated from the second German edition by Phillip Emig. Die Grundlehren der mathematischen Wissenschaften, Band 162, Springer-Verlag, New York, 1970, (Translation of previous edition [1936, 1953]). · Zbl 0199.12501 |
| [13] | C. F. Osgood, A number theoretic-differential equations approach to generalizing Nevanlinna theory , Indian J. Math. 23 (1981), no. 1-3, 1-15. · Zbl 0528.30021 |
| [14] | C. F. Osgood, Sometimes effective Thue-Siegel-Roth-Schmidt-Nevanlinna bounds, or better , J. Number Theory 21 (1985), no. 3, 347-389. · Zbl 0575.10032 · doi:10.1016/0022-314X(85)90061-7 |
| [15] | W. Stoll, Value Distribution on Parabolic Spaces , Springer Lecture Notes, vol. 600, Springer-Verlag, New York, 1973. · Zbl 0276.32014 |
| [16] | P. Vojta, A higher-dimensional Mordell conjecture , Arithmetic geometry (Storrs, Conn., 1984) eds. G. Cornell and J. Silverman, Graduate Texts in Math., Springer, New York, 1986, pp. 341-353. · Zbl 0605.14019 |
| [17] | P. Vojta, Diophantine approximations and value distribution theory , Lecture Notes in Mathematics, vol. 1239, Springer-Verlag, Berlin, 1987. · Zbl 0609.14011 |
| [18] | P. Vojta, Integral points on varieties , dissertation, Harvard University, 1983. |
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