View-obstruction problems and Kronecker’s theorem

Chen, Yong Gao

doi:10.1090/S0002-9939-1995-1277102-1

View-obstruction problems and Kronecker’s theorem
HTML articles powered by AMS MathViewer

by Yong Gao Chen

Proc. Amer. Math. Soc. 123 (1995), 3279-3284

DOI: https://doi.org/10.1090/S0002-9939-1995-1277102-1

PDF | Request permission

Abstract:

In this paper we show how the quantitative forms of Kronecker’s theorem in Diophantine approximations can be applied to investigate view-obstruction problems. In particular we answer a question in [Yong-Gao Chen, On a conjecture in Diophantine approximation, III, J. Number Theory 39 (1991), 91-103].

References

H. M. Bacon, An extension of Kronecker’s theorem, Ann. of Math. (2) 35 (1934), no. 4, 776–786. MR 1503196, DOI 10.2307/1968494

One more proof of Kronecker’s theorem

7

J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708
Yong Gao Chen, On a conjecture in Diophantine approximations. III, J. Number Theory 39 (1991), no. 1, 91–103. MR 1123171, DOI 10.1016/0022-314X(91)90036-B
Yong Gao Chen, The view-obstruction problem for $4$-dimensional spheres, Amer. J. Math. 116 (1994), no. 6, 1381–1419. MR 1305870, DOI 10.2307/2375051
Yong Gao Chen, View-obstruction problems in $n$-dimensional Euclidean space and a generalization of them, Acta Math. Sinica 37 (1994), no. 4, 551–562 (Chinese, with English and Chinese summaries). MR 1337104
T. W. Cusick, View-obstruction problems, Aequationes Math. 9 (1973), 165–170. MR 327665, DOI 10.1007/BF01832623
T. W. Cusick and Carl Pomerance, View-obstruction problems. III, J. Number Theory 19 (1984), no. 2, 131–139. MR 762763, DOI 10.1016/0022-314X(84)90097-0
V. C. Dumir and R. J. Hans-Gill, View-obstruction problem for $3$-dimensional spheres, Monatsh. Math. 101 (1986), no. 4, 279–289. MR 851949, DOI 10.1007/BF01559391
V. C. Dumir, R. J. Hans-Gill, and J. B. Wilker, Contributions to a general theory of view-obstruction problems, Canad. J. Math. 45 (1993), no. 3, 517–536. MR 1222514, DOI 10.4153/CJM-1993-027-9